Okay, what are the basics of bard grouping I should know about? For instance, I assume you hold off on damage songs until tank has aggro, but will other songs generate aggro?
Don't worry about your damage creating aggro. Your individual DPS is not likely to ever do that. You will find, especially at higher levels, that your Bard makes OTHERS in the group do more DPS, and that is one of your chief contributions. (We get special Haste songs etc. See "Krescendo's Haste Guide" in the Guides section for more details).
If you are not the puller, you will often get smacked at least once on a pull if you are still singing your buffs when the mob arrives. I wouldn't worry too much about this, unless the mobs are so badass that they can one or two smack you. Most often, they will bash you once to interrupt you, then start in on the tank. I wouldn't worry about this if you don't get whacked hard enough for the healer to need to waste mana on you.
What do you keep running continously?
As Reys said, (/wave Stretto!) there is no easy answer for this question, I'm afraid. It depends on your level (what songs are available) and what your group needs. If you'd like some specific suggestions, tell us your level at least, and we can tell you what we would use given various situations (presence of Haste, Slow, Regen etc. from other members of the group).
Definitely read some of the newbie guides about Pulling. Pulling and Crowd Control are, imo, the most fun things that Bards do. If you do it well, you will be the star of the show, and will become highly sought after for groups. Bard pulling begins with our first Lull song at lvl 8, and CC starts with our first Mez song at lvl 15, then takes a quantum leap with our first Charm at lvl 27.
Anything you have observed bad (or new) bards doing wrong?
Here's a few things that immature or bad bards tend to do:
1) Try to twist too many songs, and brag about doing so. Better to have the three RIGHT songs up 100% of the time, than to twist 5 useless ones with them dropping left and right, because you were trying to fill everyone's buff window with icons.
2) Lack of knowledge of Haste rules. LOTS of other players think they know what Bard haste stacks or doesn't stack etc. They are usually wrong, hehe. Good Bards KNOW how Haste works, and don't waste song slots on the wrong Haste songs when another hasting class is present.
3) Bad gear decisions. Bards are arguably the LEAST gear-dependent class in the game. Many of our solo techniques, for example, can be done effectively while butt nekkid with nothing but a drum. Your first priority in gear decisions should be INSTRUMENT MODIFIERS. This goes for Instruments themselves (You want Primary equippable with the best mod you can get, with the drum being your most important one), and for other items (weapons etc.) that have instrument modifiers. After instruments, you weapons should be second priority, with Armor being after both. You are not a tank. Along with main healing, tanking is one of the only things in the game that a Bard cannot do effectively.
Now, I'm not saying "don't bother with nice armor". I'm just saying don't spend a pile of coin on armor if you don't have a TDoK yet.