The happiness level of the Eevee needs to be 225 points. For every 520 steps you take with the Pokemon in your party, it will gain 1 point. For every status-increasing item you use on it (like Protein), 2 more points. For every level gained by the Pokemon, plus 3 or 5 points. Every time Blue's sister grooms the Pokemon, plus 3 points. The Hair Cut Brothers, located in the Goldenrod Underground, can also increase your Pokemon's happiness stat. How much it increases depends on the saying you get after the grooming is finished. Here is a list of how much the happiness status is increased by each brother.
For The Older Brother ($500)
If it says "looks a little happier": +1 point
If it says "looks happy": +3 points
If it says "looks delighted": +5 points
For The Younger Brother ($300)
If it says "look a little happier": +1 point
If it says "looks happy": +3 points
If it says "looks delighted": +10 points
The happiness stat can also be decreased. The following things decrease the happiness stat.
If the Pokemon faints: -1 point
If Heal Powder is used on the Pokemon: -5 points
If Energy Powder is used on the Pokemon: -5 points
If Energy Root is used on the Pokemon: -10 points
If Revival Herb is used on the Pokemon: -10 points
Also, the following do not affect the happiness stat of a Pokemon either way:
If the Pokemon is holding items
If the Pokemon wins any battle
If the Pokemon HP falls to critical (not fainting)
If the Pokemon is put in the PC
If the Pokemon is poisoned, stunned, confused, burned, frozen, or asleep
I hope I helped.