The best compliment you can give to a woman is to compliment what ever she does (what she puts effort into).
If she cooks for you compliment her cooking, if she puts effort in looking good compliment her looks, whatever she does, compliment it.
Complimenting a womans effort makes her appreciate it. Women love to know that their effort is noticed. If you need to compliment a woman, compliment what she puts effort into.
Giving compliments is something that is mandatory when you want to please someone. If you want a girl to remember your compliment, you need to say something that is unexpected. Remember that compliments will not always be appreciated. It will depend on your timing and what you will say.
You need to look at your present situation and find something complimentary based on that. You can tell a woman that you love talking to her when you have conversed for a long time. You may also tell someone that she is stunning when you know that she has made some effort to improve her looks. Basically, you can commend a woman on what she does. It will make her feel better.