More specifically a coffee date or something along the lines of a coffee date.

If you can help thanks!

I would usually call, manage to make her laugh and in a great mood, and just:
"Hey i got to hangup, I've got things to do right now, we will continue our conversation on a coffee", if she's having a good time on phone and you say "continue this", it really increases your chances, and always hang up on high note, be spontaneous. no more then 15min, not less then 3min.

Don't give her details before you get her response, or else you gave her an escape door.

If you get an "uuuuuhh" cut her off with "you seem unsure, how about saturday 7pm at balbalbal". i use this when she's like "uuuuh", thinking of a reason not meet, you cut her and make her think that you perceive her "uuuuuh" as if she's thinking of a free time to meet.
if your get a positive response just give her a specific time and location.

After re-reading you post, i guess i didn't understood your question clearly.
day 2 =

_________________
Golden Rules i learned:
1- If you complement do it a serious way.
2- If a conversation starts with a low vibe and seems not getting anywhere, be direct but not on an emotional level.

You accomplish what you want on Day 2...

What are your goals?
Do you want to get laid?
Do you want to find a nice girl to date?
Do you want a friendship?

Keep your goal in mind and be objective. Day 2 is different for every guy and every situation. I legitimately game women just to get them to come to my parties. More women = more fun. Other times, I'm actually interested in the girl and change my methods accordingly.

Short answer: Need more info to help you out.

What kind of methods would you do if you were with a girl you were genuinely interested in and wanted to date?

Also on the same note, how would your methods change if you wanted to just get laid?

Both of those on a day 2 of course.
Thanks!

If you answer the first, you can answer them all.
A girl will not be interested in a none sexual guy! she has sexual need to, she enjoys sex and crave it more then we guys do!
This is what PU is all about, there are different methods, models to follow, everyone has his own style, methods aren't one-size-fit-all, some methods may work for you and not for others. just use what matches your personality.

PU is all about inner game, this is my opinion i choose to go the natural way. If you don't have a solid inner game, you can't fake everything the whole time, girls smell it.

Now, what i usually do is, when i meet a girl on day 1, and comes day 2, i analyze if i've built enough attraction, if so, i'll just text after 2-3 days with something funny to keep her attraction level high and see where it goes, and wait 2-3 other days and call to ask her out. if her attraction level is not enough i'll call her instead of texting, tease her, crack a small joke, make her laugh and when she's in a good mood i'll ask her out.

_________________
Golden Rules i learned:
1- If you complement do it a serious way.
2- If a conversation starts with a low vibe and seems not getting anywhere, be direct but not on an emotional level.

Dude, honestly, I keep the sexual tension high without capitalizing on it right away. There is no reason to just rush into something for ME if I plan on being with her for awhile or want more time to assess the situation. Heck, I've got HB8's and 9's running around with me everywhere just to hang out with me. And honestly, if none of them work out, who cares? Being able to "command" attractive women makes you more attractive. Girls go nuts for that shit.

The only difference between that and getting laid is making your move for the close rather than "letting her off easy" and not fucking her. It's just a choice. You'll find your own way, but just work on being a confident and assertive man. Show the world who you are with certainty and tact. SeductMe is right. You need to find your own way.

Try using canned material to start (there's a whole lot of it and it helps you figure out the nature of things). I almost never pull out canned material anymore because I got used to the mindset I was in and fell into my own style.

Hope this helps.