DaCuseFrog:
There is actually a free downloadable Basic Rules pdf for D&D 5th edition on the Wizards of the Coast website. That way you don't even need web access to read up at any given time. I'll warn you that it only gives the core races (4) and classes (4), with only one subclass for each class. It's detailed enough, however, that it will give you everything you NEED to play, and once you are familiar with the basics, other books will give you a more in-depth experience.
This is great advice! Downloadable for free lets you get a good intro and some of the feel of the system without a major outlay of hard earned ducats.
When you get ready to play, peruse
Wanted - Players to find GMs looking for players in their existing games.
A great way to get in on the ground floor is to follow
Game Proposals, Input, and Advice. This is where GMs float ideas for prospective games to gauge interest in them. Be advised: you'll see all sorts of games in both of these forums, not just D&D.
It's like has already been said: don't be afraid of making mistakes (Gawd knows I've made my share here, and I'm still surviving...). Get in there and get you some!