IV Training Guide
IVs, or Individual Values, are decided upon capture or when you receive an egg and it can’t be trained. They range from 0 to 31 and are applied to every stat. Meaning; every stat has a value between 0 and 31. The higher the IV, the higher the stat. Every IV counts for 1 stat point on lvl 100 when the nature of a Pokemon is neutral. This varies if the nature is beneficial or hindering.
Example:
Seemingly the same Tyranitar at lvl 100. They both have Adamant nature and 252 EVs in Attack. This is how they look:
Tyranitar 1 with 0 Attack IV: 369
Tyranitar 2 with 31 Attack IV: 403
As you can see, quite the difference.
In terms of training, IVs are the hardest to control (barely any, if no, trainer influence). This means that even if you have the right nature and EVs, it can still be that you won't have the desired Pokemon. Thank IVs for that.
If you want more accurate calculations (to decide your newly hatched Pokemon's IVs), there are two things you can do:
Fight with it on an online match at lvl 100. This way, the Pokemon will be temporarily be elevated to lvl 100, where you can accurately read his stats and decide the IVs.
OR level it up with Rare Candies. i.e.: Save, Level-up, Read stats, Reset. This way you won't lose any of your Rare Candies, while you can still decide your Pokemon's stats and IVs. Easy ways of obtaining Rare Candies include:
Pick-Up ability at high levels.
Emerald Cloning or D/P Cloning (potentionally dangerous)
Hacking
Trading them over WiFi
Characteristics
Ever seen the phrases on a Pokemon's stat page (often scatters things, likes to thrash about, etc.)? Well, those indicate a Pokemon's highest IV. What phrase it is, is dependant on what the IV can be.
Note that they only indicate the HIGHEST IV. They will not tell you anything about all the others. Also if 2 IVs are identical and both are the highest (eg: Speed and Attack both 30), it will randomly select one of the phrases of those IVs. So a Pokémon with max Speed and Attack can have either likes to trash about or alert to sounds as a phrase, provided no other stat has equally high IVs.
Breeding for IVs
IVs can be partially influenced, and this happens when you breed. When 2 Pokemon breed, the offspring will inherit 3 random IVs of its parent's 12. Confusing? I'll supply an example.