Most of the answers are correct and I know that one is definitely incorrect, here is a general breakdown to gain prof points:

1. You only gain 1-10 prof points PER wave: Note: Slugslider fills up screen, you hit maximum of 10 prof points, you will NOT gain anymore if they respawn new slugsliders (they are not classed as a new wave of monsters even if you killed off all the original monsters from the way, and even if you level up, this does NOT count as a new wave)

2. You ONLY gain prof points as long as your character level is higher than your Rank... i.e. Rank 8 Dagger only increases if character using dagger is level 9.

3 You gain 1 prof point per successful action check above 0. You do NOT gain any prof points for a 0. NOTE: If your attack is a SINGLE action, then the "successful action check" is based on that. When using a multiple target ability, it increases your chances to gain that 1 prof point, so, using Multistrike vs 9 monsters means you have increased your chance of gaining 1 prof point by 800% (don't know how to word this to make it clearer)

4. Casting profs are around 50% faster in gaining prof points (this is NOT 100% fully tested)

5. Healing profs are by far faster in gaining prof points by my own visualisation and comparison to melee, also, it has been known that even using Tier I / II / III healing charms when character is level 150 they gain prof points just as fast as using Tier XIV healing charm.
____________________________

If you want to increase your prof points, key things to remember, keep weapon / elemental charm around 1 tier below your character level, also ensure that you do NOT kill in 1 - 3 hits. Key component, do this solo'ing, as for group play, kill as fast as possible before any other member in the party, decreasing their gain and increasing yours, or you can go with the use Multicast/Multistrike 50-75% charge / release method.

Find your best options by also keeping track of increase from start to end to give you a better feel of Prof Gain.