honestly, based on experience, the first date can also mean she's willing to give a guy a chance and/or she wants to get to know the guy better, not necessarily like him. Date number 2 (to be sure, 3) should be a guy's hint that a girl likes him. If a girl doesn't like the guy or didn't like the date, she wouldn't say yes to a second date, unless she's willing to give him a chance (indication that she's thinking about it (i.e like the guy already or getting to like the guy!)).
In most cases, this is a very positive scenario. I mean unless she has alterior motives (revenge on a boyfriend, getting a free meal), it most defenitly means she likes a guy. I personally only go on dates with guys who I think might have potential.
It doesn't mean I'm in love with them or that I'm crushing hard. Sometimes it does and sometimes it doesn't. It really depends on the guy.
However, it does mean that there is something that I do like about them and would like to spend time with them.
If she said yes, you should just assume that she likes you enough to consider going on a date with you. The rest should just flow naturally, don't over think it!
First date is like when start shopping for cars but you don't know what type of car you want yet. You are just looking at the amenities, the seats, the colors, the 4 wheel drive, how it feels to sit inside one.
She doesn't know if she likes you yet. She will make up her mind later. Don't worry about it.
If you get to a 3rd date she probably likes you.
Why? Have you been on some dates but you can't tell if she likes you?