The best compliments are of course the genuine ones, and those are the ones that any woman will value. However, I find it difficult sometime to be able to think of something that's not generic. For instance, I know never to say something like, "oh, your hair is nice"; instead, I say something like "Oh, I think how you've curled your hair looks very nice on you - must've took some time, but wow it sure paid off". Sometimes though, I just run out of ideas or cannot come up with something fast enough, and end up delivering pretty generic compliments/comments. Anyone have any tips on how I could train myself to be more receptive to things like this, or be how I could learn to improve my ability to come up with genuine, unique compliments?

If you cannot think of unique compliments, try to compliment something you genuinely like about her in an original manner instead. Also, look for stuff she's wearing and things she's been saying to you as there could be some potentially very unique and original compliments in there you could coax out.

For example, we all know "you have really pretty eyes" is a very generic and popular compliment, which makes it boring, since she's probably heard it before from other men. Instead, say something like "your eyes are striking, they remind me of the colour of the sky right after it stops raining" or "when I look at your eyes, I feel like all the little problems of day-to-day life fade away and I can't help smiling". Obviously, don't use this exact wording, it needs to sound genuine or it will feel practiced. Tweak the wording to suit the girl's feature that you're complimenting, my point is find something you genuinely like about her and then find a unique way of wording that compliment.

I generally first compliment a girl on something she's wearing, because girls spend a lot of time thinking about what to wear when they're out on a date/in a club/at a bar. By noticing the little details, it'll show her that you're a cut above the rest. "That's a really original ring, is it vintage? The colour's so exquisite, like a cross between onyx and sapphire". She'll usually get excited and tell you the story of that item and you can take it from there.

I then make a second compliment on some physical feature of hers that I genuinely like, using original or funny wording. Don't say "you have a nice smile", say "your smile is so genuine, you could run for office right now and I'd vote for you without even hearing you speak". Safest to avoid overtly sexual compliments at this stage, so don't mention her boobs, legs, etc. unless you feel it suits the mood.

No need to compliment her more than twice in one interaction, less is more or you start coming off as needy or a try-hard.

These are not hard and fast rules really, you can bend all of the above based on what feels natural at the time of the interaction.

I have that problem and one thing i do to work on it is :
I go on justjared (a girly gossipy website that has literally thousands of pictures of hot celebrities in their every day life) and i give myself a 3sc time constraint to find a genuine compliment i would give to one of them if it was on the street.

Now obviously we don't give a shit that its Beyonce or Halle Berry, the point is that you can practice for hours in the same condition you would if you were outthere only a thousand times faster.