As others mentioned, this is a class quest ability. Just stop by the Conjurer Guild in Gridania and the Guildmaster will have the quest for you.
As a WHM it looks like I'm able to pick up Thunder (A DoT) from THM and Ruin (similar to stone but weaker) as offensive spells from my level 18 THM and 25 ACN. So, nothing impressive. Fluid aura does damage with its knockback and you get a second DoT as you level. But, as CNJ/WHM is intended to be a straight healing class you won't be getting much in terms of damaging abilities because they're mostly there to give you a way to level outside of groups.
Queue for dungeons, while in the queue do Fates. Someone already explained how to get more experience from fates but I'd like to add... put your DoT up on everything you possibly can in the fates that are just a bunch of monsters and try your best to tag them as they first spawn so you can get first tag. It'll help your chances with getting gold.
If they're in your group, yeah. You also get credit towards higher medals in Fates just for healing random people but you won't get exp from the actual monsters killed.
Turn your patience levels waaaaay up. We're often the first ones that are looked to for blame when a group dies to something. Just have to keep your cool and explain exactly what happened, and if they don't like it... ignore them. You're going to get a lot of aggro on trash mobs, especially if your tank is a paladin because they don't have the best in terms of aoe threat. At lower levels it's not a big deal because you can usually take the hits easily on your own but as things get higher it gets more painful. At level 26 you'll get your sleep spell. Sometimes the tanks will mark for you to CC, that's awesome. Sometimes they won't, that's fine too but make sure you sleep anything that decides to attack you. If your spell casts are getting interrupted pretty badly while you're trying to sleep use Fluid Aura to knock them back then follow up with a sleep.
Another thing is mana management. It's pretty easy at your level but will get steadily harder to keep from ooming when you're stressed until level 38 when you get your first regen spell. My suggestion is to pay attention to the mana costs of your spells and weigh the price of using them vs higher mana cost spells. Like... is it more worh using a few cures to get people up or just casting one medica (this depends on how many people you're able to hit with the medica and what people's health is). It takes a little getting used to at first but after a while it gets pretty easy to do quickly.[/QUOTE]