Original article by @rocketbrainsurgeon
It's possible to get super in depth about angling armor, but here's all you really need to know.
BASICS OF HOW ANGLES HELP ARMOR
Here is the wiki entry on the specifics of armor angling, but I'll try to simplify it here since it contains some things which aren't as useful to know.
Angle of Impact (degrees) - Increase in Armor
0 - 100%
10 - 101%
20 - 106%
30 - 115%
40 - 130%
50 - 155%
60 - 200%
70 - 292%
71+ - Auto bounce
According to the above chart, just by angling your tank 30-40 degrees you can increase your effective armor by 15-30%. What does 30-40 degrees angle look like? Roughly it's when the gun is directly over the right or left front wheel:
BUT WAIT, THERE'S MORE
The above chart is only for one direction of angles: armor is typically angled vertically, so it gets even tougher!
Example time (simplified): the KV-1 has 75mm thick armor listed on the World of Tanks website. But the upper front plate is also at a 70 degree angle on the vertical, giving it 106% armor according to the chart above resulting in 80mm effectiveness.
That's not impressive, right? All the tanks at tier 5 have 110mm of penetration!
But now angling the tank as shown in the image above gives even more armor: using the armor calculator of a KV-1 angled gives 97mm effective armor protection! That will bounce a lot of shots from tier 5 opponents just for twisting the tank slightly sideways.
FURTHER READING ON EFFECTIVE ARMOR VALUES
If you want to see the exact values on any specific part of the tank, wotguru.com has a great weakspot guide with amazing images of effective armor values of any part of the tank.
I don't think it's required reading, because the idea will always be the same: angled armor is harder to penetrate than non-angled armor.
HOW TO ANGLE PROPERLY
Flat front tanks are tanks with armor layouts similar to the Tiger, KV-1, or T29. The benefit of these tanks is that they are very easy to angle: just slant the tank sideways to increase the armor value. The downside is when pushing forward into the enemy the armor is at its' least effective. These tanks are very common.
Pike shaped tanks have layouts similar to the IS-3, 110,
The blue square represents cover of any type: rocks, dead tanks, buildings, hills, etc. It's very important to hide the front road wheel behind cover, otherwise the enemy can shoot through the wheel, damaging AND tracking the tank!
Pike shaped tanks can have some problems with standard frontal angles around cover such as buildings since it blocks the gun.
SIDESCRAPING / REVERSE ANGLING
Whatever you want to call it, this is a way to provide what is usually an auto-bounce angle to the enemy. Recall in the chart above that angles over 70 degrees are auto-bounce, and this situation sets up those angles. CAVEAT: there's a small mechanic called "overmatch" where if the side armor is too thin compared to the shell hitting it, the shot will penetrate. The short story is this: don't try sidescraping with scout tanks or super light armor tanks such as the Leo 1 or Batchat. I've done it successfully with both heavies and mediums of all varieties, even with such paper tanks as the FCM 50t.
Taken from the wiki:
While it's possible to get a lot more complex in both information and technique, the above examples are 90% of what is needed to best use your armor.
When you know that you're going to take damage: set up an angle for the enemy. It might not bounce every time, but it's giving yourself the best odds.