With as many possibilities as DF allows, there's probably tons of different ways people play the game. How do you prefer to play it?
Do you simply embark anywhere and try to survive through all the !!FUN!! ? Do you make it easier for yourself by searching out specific embark spots?
Do you plan out and construct mega-projects?
Do you experiment with !!SIENCE!! ?
Do you mod your game to make it different?
Do you try different challenges to see if you are able to still survive?
1. I prefer to play from an "in-character" perspective. I generally have an idea of why my fortress is being settled, and what the objectives are for it. I approach every fort as though I'm going to write it up and post it here; none so far have really made it big, and I've learned my lesson about posting too soon. Still though, my forts are there to tell a story which I find fun, and usually Fun.
2. Usually I demand a site with lots of minerals, flux, and a river, multiple biomes if possible. Aquifers can be had, though I prefer at least one biome without one. What can I say, I prefer easier setups sometimes. Occasionally I'll spawn a super-high volcanism world so I can have surface magma at said cushy site, but on occasion I'll take whatever I finds and see how it turns out. Badly, most times (I'm not that great a player).
3. I plan them out, none have made it to fruition. I'm not that good at 3D design, so my plans for massive statues tend to be disappointments even before they're abandoned due to fortress death. I downloaded a program that lets you design lego projects brick by brick, and now I use it to map out a rough idea of what I want (with the added bonus of using colored lego bricks in place of colored stones, should I want a color project), which has helped me realize before I start when a design is awful, but hasn't done much for helping me design better things from the start.
4. Not much; better minds than I have that subject well in hand. I find most ‼SCIENCE‼ requires doing things that blatantly bend the rules of immersion or outright exploit things in the game which wouldn't fit in a rational world; not that this is BAD, it's just that it's hard to make a fort based on telling a story that also abuses the laws of physics and possibility for fun and profit.
5. I do, but lightly. I modded kobolds back in before Toady fixed them, and am experimenting with castes to make them a part of the dwarven race (so you could have kobold migrants living with dwarves); I like the idea of them being like pseudo pets to dwarves: smarter than dogs, but not quite bright enough to be viewed as equals. I'm considering some other mods, but I wanted to wait for a build that would be stable for some time before bothering; now might be it while he works on this big project.
6. I always play with the following restrictions: no blatantly abusing the laws of physics or "gamey" stuff to survive. No fortresses balanced on a single block, or temperature turned off so I have dwarves that can swim in magma, or danger rooms that creature super soldiers via dodging a wooden pole. No more than 15 traps in the entrance tunnel, no more of 6 of which can be weapon traps (and once the military is established, this usually is reduced to 6 cages and 3 weapons). I would eliminate weapon traps altogether if I had a strong enough military, but I never get that far under traditional training. I use my cage traps to capture prisoners for live-fire training. No "unfortunate accidents", or the like. Try to rule the fortress as though the dwarves matter, the nobles are to be obeyed, and the story I've written for it is to be followed. It's very, very challenging for me to survive. I could line up twenty cage traps and twenty weapon traps, use AussieGuy's brilliant checkerboard method for clearing out late game challenges and do all kinds of cool stuff, but I like the way I play more.