I'm starting a Bard on 5th edition. This is my first 5th edition campaign coming from Pathfinder. I can't seem to find any restrictions on cantrips. Do I automatically know all of them? Can I cast them an unlimited amount of times?
The details are all in the Player’s Handbook.
The table on page 53 lists how many Cantrips Known you have at each level. The corresponding text on page 52 under the Cantrips heading states that these are the only cantrips you know (at least, from the bard class), and that they must come from the bard’s list of 0th-level spells.
But you can cast the ones you do know unlimited times, yes. This is described under Cantrips on page 201. You still must cast them as you would any other spell, however (e.g. spend the appropriate action, cannot do so in armor you aren’t proficient in, etc).
Your class description tells you how many cantrips you get.
Check the table at the beginning of the Bard section to see how you obtain them as you progress. Bards get 2 to start, you choose those off of the Bard cantrip list and know them automatically at the beginning of your career.
You can cast cantrips as often as you want, and their action cost is what they say in the spell description (action, bonus action, etc).
I have watched a Bard continually cast Vicious Mockery for an entire combat. It was quite funny, especially since every round the player thought of new insults to the monster. At the end of the combat, the Bard had mocked one monster to death, and because of the penalties made it a lot harder to for the monsters to inflict damage.
But in essence I can see no reason why a spell caster cannot cantrip every round. Which is not a bad thing, compared to 1-3rd Ed where the mage sits at the back of the party for the entire battle, unless he chooses to lose his one & only spell for the day.