There are several parts of the process of writing an effective LD case. Their order may change depending on your experience and your thinking style. However, all of them come into play at some point.
Understanding the Resolution
This is where you always have to begin: by making sense of the resolution. Your experience level, though, dictates whether you can slide over the trip to the dictionary on your way to brainstorming, or whether you want to make a dictinoary vist the beginning of your brainstorming process.
Let's say you don't understand the resolution at all. Grab a dictionary--dictionary.com will do nicely, since it includes all kinds of definitions--and look up every important word. Or phrase, since some words shouldn't really be defined on their own.
I've made up a sample resolution for analysis.
Resolved: It is immoral to use performance-enhancing drugs in an attempt to gain athletic advantage."Immoral," "performance-enhancing drugs," and "athletic advantage" are crucial here. "Attempt" is included to maintain a reasonable burden of proof, so the Aff doesn't have to show that the drugs in question are successful.
Brainstorm reasons for and against the resolution. A value / criterion structure will arise out of the reasons. In other words, simply put "because..." at the end of the resolution, and think of every possible way to fill in the rest of the sentence. (At this point, if possible, it's wise to collaborate with a teammate, or check out an online resource for arguments you haven't considered.)
Draw a line down the center of a piece of paper--and on either side, write a "because..." for and against. Don't start with just an affirmative or negative position--instead, use both sides to shape your thinking.
Eventually, you might have 10-12 reasons for, say, the affirmative. What do you do with them? You have to choose either one that stands alone, strong enough to build a case around, or choose 2-3 that are united under a common value and criterion.
You have to ask, What are the big questions here? What are the assumptions underlying the resolution? Your primary questions, given this resolution, might include, What is the overall purpose of sport? Does sport have its own moral obligations, or does it fall under a larger moral system?
Where Values and Criteria Come In
The resolution contains important aims, ends, goals, or aspirations. Every "because..." promotes an implicit value, and points to a way to judge how that value can be achieved (criterion philosophy #1) or how to weigh that value against other values (criterion philosophy #2). (For my extended thoughts on criteria, see here.)
I find it useful to operate, as in other forms of persuasive writing, with a thesis at the center. Let's consider an example. If you have three reasons...
1. Drug use destroys fair play.All of these could be subpoints under an overarching thesis, "It is immoral to use performance-enhancing drugs in an attempt to gain athletic advantage, because it defeats the virtuous aims of competition."
2. Drug use puts winning before character.
3. Drug use is a lazy, cheap route to success.
Now you have a value of morality and a criterion of virtuous competition. Since the resolution is framed in negative terms--"immoral" instead of "moral"--each subpoint will be a criterion violation. Hold on to that for now, as we talk about other potential values.
Morality. The word "immoral" gives us a strong hint that "doing the right thing" could very well be the most important aim of the resolution. "Virtue" or "Integrity" might be allied concepts here. (Health is an important aim, but since the resolution focuses on morality, health issues would have to relate to that.)
Human Dignity. Perhaps morality isn't the core value, but rather a means of protecting human dignity (and thus morality is the criterion). If drug use degrades humanity, it is immoral.
Societal Welfare Perhaps morality is a means to ensuring the good of society, and athletic drug use has effects beyond its users. This works well with a criterion of utilitarianism, ensuring the greatest good for the greatest possible number.
On the negative, we might have...
Victory. It could be argued that the goal of sport is to win; call this the "Vince Lombardi" value, after his famous admonition: "Winning isn't everything. It's the only thing."
Freedom. Athletes, it could be argued, should be free to ingest whatever substances they wish. (Freedom could also be a criterion to a value of morality--we would judge any given moral system as valid based on its respect, or lack of respect, for human freedom. This is known as libertarianism.)
Potential criteria under a value of morality:
Equality. Drugs might "level the playing field," and overcome natural inequalities such as differences in height or muscle mass. However, if everyone's doing drugs, the Aff might respond, those with natural advantages will still rise to to the top.
Entertainment. Perhaps the true role of sport is to entertain; this is either a negation of some grand moral purpose for sport, or in fact its major moral purpose: to provide joy to spectators and participants. Either way, perhaps drugs, by allowing athletes to perform at higher levels, increase the entertainment value of sport.
Consequentialism (and one form, Utilitarianism) vs. Deontology. For how these theories play out, see here.
The basic structure of an LD case
So you have some definitions of key terms, and good reasons allied under a value and criterion structure, as expressed in a thesis based on the resolution. What then? It's time to organize your ideas into a case. The following structure is strongly encouraged.
1. Introduction. Some sort of snappy quote.
2. The resolution. Cited exactly as worded.
3. Any necessary definitions. Be sure to provide sources if your definitions are controversial or counterintuitive.
4. Any resolutional analysis. Only if you need to clarify some important aspect of the resolution that helps explain the format or framework of your case.
5. Your thesis.
6. Your value.
7. Your criterion.
8. Your contentions, in order. Any applicable evidence must be properly sourced and cited.
9. Your conclusion. It works well to call back to the introduction.
Each part of the case will be numbered below in the sample.
Michel de Montaigne once said, "There are some defeats more triumphant than victories." I agree, and  affirm the resolution, Resolved: It is immoral to use performance-enhancing drugs in an attempt to gain athletic advantage. 
For clarity in the round, I offer the following definitions: "Immoral" is defined as violating principles of right conduct. "Performance-enhancing drugs" are chemicals or substances ingested to boost speed, metabolism, muscle mass, or some other biological feature relevant to "athletic advantage," which is defined as benefit or gain in the context of a sport. An example of athletic advantage might be the ability to throw a discus ten feet further, or to run a mile thirty seconds faster. 
Also, I offer an important resolutional analysis: the resolution, since it includes the word "attempt," does not require the affirmative to show that the drugs in question provide an actual, measurable advantage. Instead, the affirmative must show that the act of taking the drug in hopes of gaining advantage is itself immoral. 
My thesis: It is immoral to use performance-enhancing drugs in an attempt to gain athletic advantage, because it defeats the virtuous aims of competition.  Sport has many forms of worth, but its greatest benefit to its participants is the development of their character. Thus, my value is morality, and my criterion is the virtuous competition.  Sport without a moral framework is just exercise.
Contention One: Drug use destroys fair play. 
One of the fundamental aspects of competition is fairness, the idea of a "level playing field." Inherent to virtuous competition is playing within the rules and abiding by referees' decisions, ensuring that both sides have, at least in theory, an equal chance of success. Although natural gifts--height, muscle mass, endurance--are inequitably distributed, there are virtuous ways to overcome the odds--and this is key--that are inherent in the competitive activity. Practice, determination, effort, on the field and in the gym. Drug use turns sport into a competition among chemists, and, mostly, a battle of bank accounts.
Contention Two: Drug use puts winning before character.
The old saw, "It's not whether you win or lose, but how you play the game," is a central axiom of virtuous competition. Drug users, by relying on chemical cocktails to improve their performance, in essence are fixing their eyes on winning above all. This has multiple effects: it makes them more likely to cheat in other instances--tripping an opponent when the ref isn't watching, knowing that the win matters above all. It could lead to boorish or selfish or even self-absorbed, limelight-hogging play. Instead of playing for the spiritual, emotional, or even physical benefits, winning becomes the only motive, and all else is sacrificed.
Contention Three: Drug use is a lazy, cheap route to success.
The most important virtue of competition comes from the challenge. By reducing the natural barrier to success, the drug abuser has to work less to achieve the same results. This not only negatively affects the individual, but harms teammates, who will be more likely to take the lazy route, and even harms society, as youth, who look up to role models, decide to imitate their indolence.
As we have seen, the aim of sport is not exercise, or fun, or even eternal glory, but the development of moral character. Performance enhancing drugs, by corrupting fair play, by promoting winning above character, and by shorting the challenge, destroy the virtuous aims of competition, and thus their use is immoral. For these reasons you must vote affirmative. I now stand open for cross-examination.
(Should this or something like it ever become an actual LD topic, you might consider reading this debunking of steroids stats. Also potentially of interest: a libertarian debates in favor of PEDs.)