There have been some good suggestions regarding how to choose an amp.
This is what I do:
1) Research because I don't have the cash to buy everything to try, nor do shoppes close to me have a large selection to audition.
1 a) What to research? Well, first and foremost, figure out what the entire chain is all about, what power output the player has, what power requirements the headphones have and then go from there. I will disregard all those amps that don't meet a basic requirement even if it might sound good because at some point, the sound should/would suffer if power demands become too high (or current demands, voltage whatever).
1 b) Sonic signature. I read a ton of reviews and I focus on key words that are used to describe music in the same way I like to hear music. I focus in on those amps that seem to exhibit such traits in conjunction with the phones I'm going to use with it. I try to read as much as possible to get a concensus.
1 c) Who wrote what. Next, I start scouring the site for posts or threads from a particular person who might have condemned an amp or given one a glowing review. I look for consistant pessimism, criticsm, hyperbole, infatuation and fanboyism. I then examine the profiles, associated gear and listening tastes. Once I glean as much as I can I feel safer in pulling the trigger.
2) Head to meets if possible. Listen and get an initial feel for the sound. Though it might not be your entire system, if you have your own headphones or the type you want/own then at least you can get an idea of the sound. Meets are generally not the best place for critical listening but there is no doubt that one could at least figure out if they detested something.
3) Buy and try. This is really where the meat of the process comes in. In the end, no one's opinion matters except for yours and yours alone (unless you will be sharing your kit with a friend/significant other). Listen listen listen! If the amp turns out to do what you want it to do keep it! If not, sell and retry. But! Don't hope that an amp will magically transform a system into something divine, in my opinion the two major components in a chain are the source and the transducers. They will make the biggest most dramatic sound changes. That said, if you do like something, even if most don't, don't be a lemming and sell because it is not the "in" amp of the week/month/year. Enjoy what you have, be happy and listen to more music!
4) Before selling, (particularly if one is jonesing to spend some cash on a new amp even though the present system sounds perfectly fine) reread past reviews, even if the reviews are a decade old. Read and reread, fall in love with your gear again. This might curb any feelings of "gotta have something new."
If there is one thing I have learned from "older audiophiles" guys who have been in the hobby for decades, it is that the upgrade path is often not really a ladder journey but more of a plateau jumping journey. There are plenty more sidesteps (and very often steps backwards) vs. really moving up the rungs of a ladder. Once one attains an excellent synergy, plugging in a new amp, even if the old one was $500 and the new one is $25000, it might not jive as well as the old one. There is a LOT to say about system synergy. It is in the end, the most important aspect. The best pieces in the world won't necessary combine to make the best system in the world.