I decided to post this as an article rather than respond with a comment for reasons which will become evident.
""Okay, so, I am thinking about getting into 40k. I am really intrigued by the Eldar fluff, but am having trouble figuring out exactly how they work tactically. Are they mostly fast-moving, with a lot of long-range shooting? Or do they rely more on assault? I'm getting conflicting messages from the Internet, so I thought I'd ask a reliable source. Kurthl337"
Well, first of all thanks Kurthl337 for considering me a reliable source! I know what you mean about getting mixed messages from the Internet; this can be very frustrating for someone trying to learn about the army. I'm guessing you already read my article about hype. If you haven't, I suggest you do. It should clear up some of those mixed messages you're getting!
The short answer to your question is "all and none of the above", but if you read on I'll elaborate on that...
Answering your specific questions: The Eldar have some fast moving units (jetbikes, fast skimmers and tanks), but most of their guns have a range under 48" and very few weapons with Barrage, so although their overall mobility makes up for it, I wouldn't call them "long range". Similarly, they have some excellent assault units, although they all require support of some kind to do better than trade a unit with the enemy. So each unit will have a particular strength and a particular set of weaknesses to offset those strengths. However, there is no equivalent to a space marine tactical squad in the Eldar 'dex; there are no generalists!
With the Eldar codex you have a broad selection of units with which to make almost any style of army imaginable.
The core philosophy of building an Eldar army is this: every unit must function as a part of the whole army. For example, Dire Avengers support Howling Banshees by softening up a unit with a well-timed Bladestorm (+1 shots per model) before the banshees charge in. The Dire Avengers can also help in the assault if you bring an exarch with Defend. Putting them both in wave serpents also gives these units a nice mobile support base which can serve as transport, a heavy weapon platform, or even cover when used to screen against enemy units.
Each unit must support the other in some way; there is no room for a unit whose talents fall outside of the army's main strategy. For example, if you were running a heavily mechanized army with infantry units carried inside fast skimmers, you would have a hard time making a foot-slogging unit like an avatar or wraithlord work with the rest of the army. I'm not saying it's impossible, just very difficult. Every unit which does not have synergy with the rest of the army actually holds the rest of the army back!
If you study the codex you will see that it's pretty easy to build an army along a particular strategy. Fritz is an excellent Eldar general and constantly searches for new ways to exploit the Eldar's aging codex in the current Warhammer 40k rules set.His theme-based lists can be very powerful, although they do take a lot of practice to learn their correct use.
A little self-knowledge also goes a long way. Knowing what your play style is can help you decide what kind of army to build. Once you know what kind of army to build, the rest will probably fall into place pretty quickly. If you haven't figured out what play style suits you best, then you may want to start with a more robust army, so that you don't spend the next 8 years trying to figure out how your army should work, like I did. My favorites are mechanized eldar with many tanks and transports or jetbike-heavy lists; infantry "footdar" lists don't work so well for me.
Anyway, I hope this answers your questions. You can build almost any kind of army imaginable, but the whole of the army must be aligned under a single purpose.
Grow them Eldarses! They're a dyin' race!