How much xp/prestige do you gain at a gym by training?

The xp is 10% of the prestige that you get.

When training at a gym you will get 500 prestige per pokemon you defeat with equivalent CP value. ie. If you beat a 100cp pokemon with a 100cp pokemon, you will get 500 prestige.

You will get more than that if your Pokemon is lower than the one in the gym and less if it is higher.

How much less/more I am not exactly sure but as pointed out by Sobrique the formula may be P * D / A if the defending pokemon is of a higher CP. Where P is a multiplier of 500, D is the defender's CP and A is the attackers CP.

If the attacking Pokemon is higher then P is reduced to somewhere between 250 and 350.

The maximum you will get is 1000 prestige if your Pokemon is at least half the CP of the one in the gym. The minimum is 100 prestige which is when your Pokemon is double or more of the CP of the Gym's pokemon.

You cannot lose prestige by training at a friendly gym.

According to heavy.com, it is:

• When your attacker has a lower [or same] CP than the defender:
  500 x (Defender CP / Attacker CP)
• When your attacker has a higher CP than the defender:
  310 x (Defender CP / Attacker CP) – 55

and the max is 1000 per defender you beat.

Also note that the attacker's CP is the highest CP of your 6 Pokemons, even if you didn't use it. For example, if you beat a CP 1000 Arcanine using a CP 500 Vaporeon, but one of your other 5 Pokemons that was chosen for battling have CP of 1100, then the CP 1100 is used to calculate the prestige increased, instead of using CP 500. As a result, if you intend to beat only that Arcanine, then choose your other 5 Pokemons to have CP at or lower than 500 CP if you want a prestige increase of 1000.

The XP is 10% of the prestige increased.