This is how it works where I live, your region may vary.
In-person works better than the phone. It takes time and leg work and you often have to go back a couple of times. Find out who the venue's band booker is and find out when they are there and when they want to talk to you (you can do this part on the phone, just don't call when they are super busy).
Once you have that intel, talk to that person face-to-face if possible and take them a promo package with a DVD of your band playing. It's a big pain in the ass but getting established as a local band is a big pain in the ass, period.
I've even gone to places as a customer a few times until I got to know the bartender and then chatted them up about the band booking situation. As long as you are honest and not pushy or slimy about this, this can help, too. Just remember the bartender isn't the booker and you don't ask him or her to "put in a word" for you, just get the booking information and put in the word yourself. Don't oversell your band but don't be too modest either. Just be honest. They've heard it all. Every new band thinks they are going to be the next big thing.
Each venue can have a slightly different protocol and it can sometimes be a touchy situation. If you're lucky you'll find a very open and friendly booker or a venue that is also new and trying to get the band thing going.
Many established bookers in popular venues are lazy and once they have a regular reliable rotation of bands they aren't too keen on rocking the boat. They know it's very competitive out there and they put all the work on you. They will fail to return calls and placate you and outright lie to you at times. You can get angry or you can just be patient and persistent. The latter usually works better for having any shot at getting booked at these types of places.
Sometimes you have to wait for one of the other regular bands to break up or screw up or just flake out. You can sometimes get put on a list as an "alternate" band to call up if somebody flakes, but you have to be willing and able to play on very short notice. This can be a big problem if your band members have jobs and lives outside of the band.
You can also offer to open for other bands. This can work great (less work for them, exposure to a new audience for you) but don't expect to get paid. Some bands don't like openers or won't use them at all. However, some of the ones that play several times a week will gladly use them. They get tired of the same 3 sets over and over and don't mind the help. The really nice ones will give you a cut of the pay but don't demand payment as a new band.
Remember that 99.9% of venue owners only care about the bottom line and they want the band bringing customers and keeping customers there and drinking. You could be the best band in the world but without customer asses in seats and customer wallets open, they really don't care.
There are a few venues (thankfully not many) where they expect you to pay to play. They will sell you a bundle of tickets and then it's up to you to turn around and sell those. I recommend avoiding these places. For some bands it ends up being their only choice, but it should be an absolute last resort. Being a semi-pro musician is expensive and low-paying enough, if you have to pay to play you're doing it wrong.
You may also run into a micro-managing venue where the bar owner or band booker wants to give you very specific instructions on what to play, how to play it, where to set up your gear, how to run your mix, and so on. These are wannabe music producer types who are role playing a fantasy at your expense. I would avoid them too, if at all possible. Sometimes you have to deal with them if you want to play. If this happens just play along until they get bored and or distracted with customers and employees. This type of person can be very pissy if you don't respect their Cartman-like egos, and they will kick you out of the venue for minor reasons.