junimo

Here's a link you might find useful: https://wiki.pokemon-vortex.com/wiki/Happiness
 
Basically, you want to have the Pokemon participate in battle at least once, without fainting. Do that until its happiness goes up.
 
You can get four hearts at max happiness, and the fourth heart only takes about half as many battles to get as the first three. One battle is worth 1 - 2 happiness points and you need 255 total happiness points to get to max happiness. For example, if you want a silveon you want to take your eevee through 128 to 255 battles where it can participate without fainting.
 
Note: Most pokemon only need 3 hearts to evolve, not four. So they only need 110-220 battles. Silveon is the only Pokemon I can think of that needs 4 hearts to evolve.
 
Pro tip: there are dummy training accounts that can be very useful. In PvP search "type[your Pokemon's type]". Example - say you want to get three hearts happiness to evolve a buneary. Go to the PvP search screen and search "typenormal". Then take your buneary through the battle. Lather, rinse repeat 128-255 times until it reaches your happiness goal.
 
These accounts are especially useful for normal type Pokemon that need friendship training since they have full immunity.