This is the problem Apple is grappling with right now. I'm hoping that they'll have some answer for us this year that helps us deal with the number of competing apps in the app store.
In the meantime, I have a few strategies for finding an app that meets my needs:
Use the app store search.
If you need your ebook reader to support epub, bookmarks, notes, and dropbox, simply type, "epub bookmarks notes dropbox" in the search field of the app store. I like to sort first by rating and check out the highest rated apps, then by popularity and check out the most downloaded apps. Note that sorting by rating and popularity are only available on the iPad.
I read the reviews, both at the high rate end and low rate end to get an idea of the types of features people are excited about, and the types of problems people are experiencing.
I look at the most recent update notes, and see how long ago it was last updated to get an idea of whether the developer is taking an active role in maintaining the app and is responsive to complaints, or if it's an old app that works, but probably doesn't have new features.
At that point the only thing to do is to try out the ones that look most promising. Many apps offer a trial or ad supported version, so the trial can be free in many cases. For others, you'll have to pay a little to try them out, and if they don't fit your needs you've lost a little money and time, but remember that you're picking an app that should fit your needs for a long time - when you find it it will be worth the effort and money you've spent on other apps looking for the perfect one.
Use internet reviews/forums
Do a google search for "best ebook reader ipad" or similar, and you'll often get dozens of "top ten" style lists from people who have spent some time not just reviewing a few apps, but comparing and contrasting them. You have to do a bit of wading, and you are going to have a hard time finding less popular subjects, "best lawn care app" isn't going to give you such collections because few people will have taken the time to check them out, even though many exist onthe app store.
Ask in appropriate forums
This site, Ask Different, does permit apple and iOS specific product recommendations, for instance, and there are many other forums that are fine with such questions.
You can check out the tag software-recommendation to get examples of the style of questions allowed here. The tag has this note which might also give you tips on asking for a recommendation:
Recommendations can easily be subjective and local to one person or time. Please be specific about function and broad about timeframe so that your question, once answered objectively, is of use to the community.