First off, welcome to the community! You made the right choice in coming to TFTV.
http://comp.tf/wiki/Main_Page is a good place to start. It has a ton of guides on classes, maps, players, events, and other things.
One of the first things to understand is how the game is played. Pub tf2 is wildly different than comp tf2. There are two main formats that we play competitive in: 6v6 and highlander. 6v6 is probably the one most comparable to any other esport, and is the one we focus on in TFTV. 6v6 is played with 2 scouts, 2 soldiers, a demo, and a medic. While there are many different map types in TF2, in 6v6, the ones most played ar Control Points (also known as cp) and King of the Hill (also known as KOTH). If you want to get familiar with the maps we play, check out maps like cp_badlands, cp_granary, cp_snakewater, and cp_process final, as they're all official and rotate on valve servers (and community ones). The community also has updated versions of stock maps (like koth_viaduct) that fix balancing issues and FPS problems. While there aren't too huge of differences between the stock version and ours, it's important that you look out for them and understand how they're different. Our versions of maps aren't stock, so you'll have to get them from somewhere else.
Highlander is a 9v9 format that utilizes one of each class. It plays more gamemodes, like Payload (pl_), and is often easier for people to get into. However, Highlander doesn't have an official ESEA League, or LAN. It's more accessible, but you're not likely to get as far competitively with HL as you would for 6v6.
As for practicing, there are several methods. One is called MGEMod (or just mge). It's hosted on community servers (you can click on the servers tab at the top to see them all) and is a 1v1 training mod. It simulates the control points of several maps for a 1v1 DM fight where you can learn about positional advantage as well as get your raw aim up to par. Another popular method is Deathmatch (or DM) servers, with instant respawn, small maps, and 8 players to a server, to simulate the chaotic fights that TF2 is known for.
As for places to practice, there are several as well. The lowest-level is http://tf2center.com which is a lobbying service for lower level players (although it's currently embroiled in some controversy). KevinIsPwn and company also run 6v6newbiemixes which are very good for getting into sixes. More info can be found here! http://steamcommunity.com/groups/na6v6newbiemix.
Once you start getting better, you can head over to http://tf2pug.me, but this is generally used for people that at least have a season of ESEA experience.
Hope this guide helped!
and i swear if kevin posted before me