Hello
Can anyone tell me a fast and good way to level pets please?

depending on why you are asking it for :

if you are looking to change one/multiple pets on your team do once at the time in the last rea you have unlocked, keep the newbie in second or third position to prevent it getting ohko in the process.

If you want to level your team up but dont gain exp anymore you'll have to wait a festival zone to do so tho a change of items / a check of your proefiencies may give better results.