I'm a 4-plus years salsa dancing vet and I let me tell you something: While you can sort of get better slowly by practicing at home watching videos, the crude reality is that the best and fastest way to improve is to just swallow your fears and go to the clubs like if it was a religion!
These are a few things to keep in mind.
Not everyone is a pro, so you are bound to make friends who are your level who would be happy to dance with you.
The most expert dancers are human, and even if you had a horrible dance with one, and stepped on him/her. They will forgive and forget, which means you can ask them again and will likely say yes.
Trust me on this one: forget about getting a big repertoire of moves at the beginning, just get a handful and get the basics extra solid! Everyone prefers 100 well done crossbody leads than a handful of crappy around-the-worlds and painful copas.
Work on keeping your back straight, butt out, knees bent, keeping the beat, and being smooth and firm at the same time.
Most importantly, have fun! Don't stress! Everyone screws up! just laugh it out and keep going!
The crazy turns, arm knots and all that will come on their own, trust me on this one.
Girls tell me they love dancing with me (they line up to dance with me I swear!), because I'm smooth and firm, and I only do moves I know I can lead.
In a nutshell, go out, work on basics and have fun!