I recommend all resources here to help you get better at League of Legends. Most of the resources are free. The ones you pay for are worth it.

Replay Feature

Replays are the most important tool you can use to get better as a player. No other tool can impact your game play. See Riot's replay FAQ to learn how to use their replay system. You have to do the work of reviewing and analyzing your games otherwise watching just becomes entertainment.

SoloMid.Net

SoloMid.Net is my favorite place for champion-specific guides and builds. Anyone can write a guide – and many do – so there is a lot of bad advice out there. Pay attention to the featured guides on the SoloMid website (mostly written by pros), be skeptical of the approved guides, and only read other guides for ideas. Never take advice as gospel. Read about your favorite champions at: solomid.net/guides.php.

LoL King

This tool is good to research player history real-time. LoL King instantly updates from Riot's servers. What I like about it is you get to learn a player's best champions in the past week and see all the neat stats like kills, deaths, and win-rate. The real cool thing about LoL King is they provide charts like the most-played champions, the lowest win-rate champions (new champions are always there), bottom-lane synergy, and lane matchup statistics all with neat filters like regions and medal rankings. The data helps you pick well in solo queue.

LoL Counter-Picks

LoL Counter-Picks is a community-driven site to counter-pick. The suggestions are questionable because any player signs up to the site then votes on who counter-picks who. As with any counter-pick, factor in how good you are with the champion and understand why it is a counter.

WTFast

WTFast is a unique tool you download to improve your game connection. LoL players have found this betters the speed of League of Legends, reduces disconnects, and manages lag. If you're not happy with your connection and want to optimize it, I encourage you to signup.

LoL Nexus

LoL Nexus features a real-time match lookup tool that can display info about current games. Get a feel for the player you're about to verse by using the tool during the loading screen.

LoL Creep Calculator

Run the LoL Creep Calculator on a second-monitor or as a background program when you play LoL. It will help you track last-hit goals to keep you focused.

VoIP

Communication is key to pre-made games so here's a selection of good, free chat programs:

  1. Vent
  2. TeamSpeak
  3. Mumble

Wiki

The League of Legends Wiki is excellent when you want a technical understanding of anything in the game.