Set up your time
It seems like a simple thing, but so often we set up the trial, we download the client, and then we forget about it for two or three days. Or we don't even patch the client right away. Or we get started and then remember that we have a week's worth of solid dungeon runs scheduled in another game, and off it goes to the "never played" pile.
Those are the obvious elements. If at all possible, you want the client installed and patched when you start the trial period, that's obvious. But there are more subtle concerns than that. Take a look at the game's maintenance schedule and try and set things up so you'll hit as few unplayable days as possible. Keep peak times and events like holidays in mind before you sign up -- holidays can give you more people to interact with, but it can also give you more lag and potential server instability. Ideally, you want to be playing at a time that will give you an idea of the game in normal operation, rather than an unusually heavy or slow period.
Do your homework
Before you start playing the free trial? Read about the game. Not just the maintenance schedule we talked about above, but about the systems. While some sites give a great deal of detailed information about the game (City of Heroes) and some don't (Final Fantasy XI), the official sites are not usually a strong resource. You want to find forums, fan sites, wikis and other repositories of knowledge. Places not overseen by the company, where people will talk about the game however they want.
What are you looking for? Two things: the game's community and how it feels, and information on how to make your trial experience as painless as possible. If something within your preferred playstyle is considered searingly overpowered, that's where you should be aiming at first, to see if you enjoy the game. Try the more challenging builds and classes later, after you've gotten a sense of the game as a while instead of just the first few levels. There's no reason for you to make life hard on yourself when you learn a new game -- the learning curve will usually be plenty hard enough without you adding to the trouble.
The trial character is just that
You get attached to characters you make in any MMO. That's a given, no matter how much you might claim that roleplaying is evil. It's just human nature. But you have to fight that urge for the trial period, because this character is only there for you to see how the game runs. That means you owe it to yourself to have them do stupid things.
Run into huge packs of enemies -- you need to know what you're going to be able to handle, and you want to see how harsh it is when you die. If you get a rare drop that high-level players will pay dearly for, sell it and roll in cash at low levels. Sell off anything that doesn't have an immediate use, even. We've trained ourselves to hold on to everything and avoid trading any sort of long-term benefit for an immediate gain, but this character is never going to hit the endgame. They are there for you to experiment with the game and possibly kill repeatedly, not for building a foundation.
Break out of your social comfort zone
These days, free trials usually have some limits based on trying to prevent people from using them as RMT-droids. You can't talk in all forms of chat, and you don't have a full suite of options open to you. That doesn't mean you can't talk to people at all, though, so take the opportunity and speak up. It's too easy to move through the game during the trial with your head down, and then stop playing because all of your friends play a different game. If you want to put down roots, make friends, and if you want to make friends, you're going to have to speak up.
Ask questions. Unless you're playing World of Warcraft, most people in the game will be happy to tell you all there is to know about the game. Join parties after getting random invitations. Be friendly. If there's a general area discussion channel, talk about things with people, and if no one is talking, start up a conversation. Friends can make all the difference in an MMO, easily making up for any number of failings the system itself might have. If you're going to decide not to play the game, let it be because you dislike the game itself.
Just try the game
The goal of all these points is twofold: to make the actual play experience easy and straightforward, and to give you a solid foundation of knowledge to base your choice on. Where you have a choice between something difficult and something easy, opt for the latter. Where you have a choice between trying something new and possibly unique to the game or doing the same thing you always do, opt for the former. Put the game through its paces in earnest, and you'll wind up ending your week-or-whatever trial with a much clearer idea of how the game plays.
Above all else, these guidelines and suggestions are just that. Your main goal is to have fun, and all you really need from the free trial is an idea of whether or not you're going to enjoy dropping money on the game on a monthly basis. That makes the best possible tip to really devote yourself to trying out the game. Clear your schedule a bit, expect to be a bit uncomfortable and unfamiliar with the controls at first, and dive in. Don't use it as a spare time killer, or when your server is down, or anything of the ilk. Let the trial and the game stand on its own, and who knows -- you might have a new favorite in the making.