DoTs are Ailments and you need to spec into them for them to do the endgame damage because you can apply Ailments on more than just skills. There are skills that also get bonuses for having Ailment stacks on enemies, like Bladestorm has a trait that increases its damage per ailment stack on an enemy and it's usually a pretty hefty sum, making it useful to stack the DoT even if the DoT doesn't do damage. Of course, you could also just use Aether or Shadow damage that stack an Ailment that reduces speed or increases damage taken of the enemy instead while also being able to stack, so they'll feel a bit more useful than the small DoT.
To go with DoTs, you'd need to go into the part of the tree that allows you to proc two different ailments on the same hit. allows the ailments to crit, and also procs multiple stacks of the ailments. The multiple stacks is vastly less powerful compared to before since it only adds a little bit extra, but it's still a multiplier.
You also typically use ranged weapons and grab the +1 projectile node so you increase your proc rate by adding the extra projectile to your skill or basic attack. The Pistol+Shield is a good set up for non-casters since it has a shotgun, which gives you a very high proc rate early on even with a low chance and when you get the crit node, more hits means more chances to get crit DoTs.
You basically need to look at your skills and see what ones can proc more and of what. Currently, the best DoT is Bleed+Poison. The overall best ones are Bleed and Burn, but they share different damage multipliers/increases since Bleed is Material and Burn is Elemental, so it's best to go Bleed+Poison or Burn+Shock. Burn+Shock has inherent AoE since both damage nearby enemies on top of the main target, but this makes it weaker on Bosses. This would be a nice difference between the two if it wasn't for the fact most methods of applying Ailments are AoE and will hit everything anyways, thus not needing the extra AoE. Like even for Casters who you'd think with Elemental Spells would focus on Elemental damage are better off changing their spells to Rend and Toxic for Bleed and Poison since they do more damage. Bleed ticks every .5 seconds and Poison at .9 seconds to Burn's .6 seconds and Shock's 1.0 seconds.
TL;DR, DoTs are useful, but Bleed+Poison are really the only way to go since there's better multipliers for them. Burn's only plus is a node that removes 5 Burn stacks to do 50% more damage on the hit that removes them and Shock has no plus at all really. You have to spec specifically into the DoT to make it do damage and not much will multiply their damage enough to be noticeable. Personally, I just use Fireball with extra projectiles and the Piercing trait since it has a 2.5x multiplier to ailment chance, so as long as you're at 40%, it'll 100% apply. Change it to Poison damage and put Bleed on your Weapon or to your spells for the Bleed, then use Plagueburst with the toxic cloud trait so things die and cause clouds that will poison and bleed things without extra casts.
