There's no way to tell the exact number, but you can get ranges for happiness.
You can use the friendship checker to tell a pokemon's happiness. It shows 0-2 hearts to measure happiness. More hearts mean a happier pokemon.
there's also a Person in the games that will rate their happiness, giving you a general idea of where your pokemon is. Here are the messages and what they mean.
Message--------------------------------------------------------Range
"It looks really happy! It must love you a lot." ............ 250-255
"I get the feeling that it really trusts you"..................200-249
"It's friendly toward you. It looks sort of happy."...........150-199
"It's quite cute."................................................100-149
"You should treat it better. It's not used to you."............50-99
"It doesn't seem to like you at all. It looks mean." ..........0-49
The messages differ slighty from each game, and those differences can be found here.
There's a woman in eterna City who will do this for you, and she's the one that gives you the pokeapp.
On a side note, this is how I bred my Umbreon to evolve very quickly-albeit, pretty expensive due to the EV items.
-Breed an eevee, then hatch the egg (its happiness will start at 120)
-Give it 200 EVs with Vitamins as you see fit. I used 100 defense and 100 special defense. You'll get several points just for that.
-Level him up to say, 15. this increases by +3/+4 per level, then +2/+3 when he's over 200 happiness
at level 8= 201-206
at level 15=215-220.
This one is helpful since he'll be at level 1, and levels up very quickly.
So by level 20, he should evolve. You could also use a soothe bell to do the job faster.
