Must-see video:
http://www.youtube.com/watch?v=Bu2PWIowvZI#!

Info for new players:

Turn on the 'server side reticle' in the game options

Suggested Reading:
Battle Mechanics (includes spotting/camo system, a must-read):
http://wiki.worldoftanks.eu/Battle_Mechanics

Tank weakspots:
http://forum.worldoftanks.com/index.php?/topic/49967-for-people-that-would-like-to-learn-frontal-tank-weakspots/

How to scout:
http://forum.worldoftanks.com/index.php?/topic/122753-absolute-beginners-guide-to-being-a-tier-4-scout-in-a-tier-9-match/

How to evaluate a tank's performance beyond the numbers:
http://forum.worldoftanks.com/index.php?/topic/187552-how-to-evaluate-a-tank-better/

Tier 1 and 2 are a clusterfuck, but use it to learn the controls and maps.

Tanks start to get their 'real' roles at tier 3 and onwards.

It's not a race to tier (I)X. Find a tank you like, and [spoiler]have fun[/spoiler].

Radio may seem useless at first, but they do have their benefits. As long as your and a teammates' radio signals overlap, you can see eachother on the minimap, and you see the enemy tanks the other has spotted. So this is particularly useful for Scouts, Tank Destroyers and SPG (artillery).

Popular and very effective low-level tanks are the Marder II (German TD) and SU-26 (Russian SPG).

If you play a light tank, you will encounter tanks way higher then yourself. This is because they are SCOUTS and not front-line brawlers.
Scouting = get a good radio, good camo crew/camo net etc, find a good spot on the map and park yourself in a bush. If your crew is max camo, enemies that are over 50m away will just not see you, while your whole team can see them thanks to you. You will get extra exp for every enemy you team kills while you're spotting it.

It's not just point and shoot, there are extensive mechanics going on for each shot, distance, angle, armor, location and angle of impact all matter.

Learn the basic weakspots, this will save you a lot of frustration. Machine gun slots, view slots, cuppola, lower glacis plate, tracks, backside are in most cases weaker spots in the armor.

Always bring a few high explosive rounds. Switch to them if your shots bounce no matter what, you probably won't see their hp drop, but there's a chance you damage a module or even kill crew members.

If you see a teammate struggling with 2 enemies, help him by shooting the same target as he is. You get exp based on damage, not kills, and 2 enemies at 50% are way more dangerous then 1 at 100%.

Don't be afraid to run from a superior force, or to 'camp' and protect a flank with a TD. Rushing in just to die helps no one.