These relationships take on a more light-hearted and pseudo-romantic tone and are completely optional for the most part.
Usually, this will involve a burger at Burger Shot, or perhaps some beers and darts at a local Irish pub. Regardless of what it is, try to diversify each time you go out with a girl, and be especially mindful to listen to their feedback as you walk around and drive around at all times.
This is the best way to get plenty of insight into what a particular girl thinks about certain activities. If she loves it, you can go back another time, but not the next time. Perhaps the most difficult part of any date in GTAIV is the end, when you're bringing a girl back to her place (likely swerving all over the road and killing innocent bystanders since, y'know, you're drunk).
This is the best gauge to see how well you're doing with any girl.
As far as receiving calls from prospective dates, you can answer the calls and let them know that you do or don't want to go out, or you can do what I do in real life—dodge the calls and go to Hobson's Choice with Dave Clayman instead.
There are two different kinds of primary relationships in the game.