Speed comes from economy of motion and practice. Economy of motion comes from practice. You're starting out, the fact that you can't play blazingly fast is to be expected.
There are software programs (I use Anytune) that will allow you to take an mp3 or wav file and play it faster or slower (without altering pitch) and you can also transpose. Load the tune in that you want to play, and slow it down until you can play cleanly.
If you're in doubt about what speed to start at, lean towards slower. Play it a bunch of times at that speed, concentrating on making sure you can play cleanly. Then, and only when it gets easy, turn the speed up a bit - I think Anytune goes in 5% increments. Play that for a while, again concentrating on playing cleanly. When it gets tough, take a break. Come back and start over, at the slow speed. Eventually, you'll get there. Don't try to get really far in one session - patience and persistence are key (Haste makes waste).
I've been playing for over 40 years, and I still use it to build speed - I don't strive to be the guy who can play the fastest, but if I run up against a tune that's a bit tough, I will work on it until I can play it cleanly at speed, and then run it up in increments to 120% or so - the point of building speed to me is not about being blazingly fast, it's about having enough "headroom" in your technique that, when you go on stage, you're not running at the limit - everything is in control and well within your capabilities.