So I finally found a club where they do open mics. I don't know how to sing live . It going to be my first time. Do I sing live with the full song playing meaning with the recorded vocals. Or do I need to make a separate track with back up vocals? Any tips about this?

Practice at home first.
 
Or make sure the bar is in another state or province - haha!
 
Last but not least - don't take her with you if it's your first date.
 
Better to leave her at home and tell her about it the next day in 'your own words'.

Lol no it actually down town. How about the track ? Should I include vocals?

Do you mean the original vocals of the song?
 

Yes

At an Open Mic people will be expecting to hear you perform, live, not listen to a recording. Get practicing...

I should point out that "open mic" generally means that anyone can get up and perform (with or without a mic), it's not meant to be a definitive statement of "here's a mic, go sing.."
 
Singing to pre-recorded backing tracks (with or without the original vocal) is usually called karaoke,  an open mic night may not even have any equipment to play backing tracks unless you take your own.
 
There are a few open mic nights at pubs near where I live and all you get is a couple of mics and a small p.a.  People turn up with their guitars (acoustic or with a small amp) and play their own stuff or set up jams with the others that turned up.

If singing is what you want to try, go find one of the many available karaoke bars and give it a whirl.  Everyone expects the person singing to suck which is good for you in two ways:  If you DO suck, no one will care, but if you don't, you will definitely stand out and people will appreciate it.  As Karen pointed out, "open mic" nights are usually for people playing instruments to jam together.  Once you're comfortable singing in front of people (and you don't suck), then audition to sing with a band or build your own.  Even the best singers needed to pay their dues before being "discovered" and elevated to better bands, venues and, eventually, fame.
 
 

yep - I third that!  open mic usually means a PA is available to plug your equipment into.
 
it's possible they have a CD player plugged into the system that you could use, but you'd need someone running the CD player and PA to do it.
 
DON'T have a CD with the original vocals still on it - they are going to want to hear YOU singing, not you singing on top of the original artist.