DDO is about grouping and being able to make your own groups is a needed skill.
Generally it's to your advantage to add people. You get the same number of items per chest whether solo or grouped and you'll see a lot more chests grouped because you'll clear content faster. You'll get the same experience for doing a dungeon too plus they may do things like disarming traps or breaking crates that earn you more experience than you otherwise would have got in a solo clear. Plus you'll clear faster.
In other games you can adopt a pattern of grinding something solo while you keep an eye on the lfg channel/tool but here I think you will have a much much better experience if you're able to take the initiative.
Starting a Party
To start making a group press O. This brings up the Social panel. Grouping is the first tab. (It's also one of the buttons at the top left).
I always uncheck Show Groups I am not eligible for and check Hide content I don't own. It's unfortunate it defaults to showing you irrelevant groups, but Turbine have to get you to spend points somehow. It's nice if you have alts too.
At this point if you're lucky you will find a group you want to join and can skip the rest of this post.
Let's assume you don't.
First you can ask anyone on your Friends list or in your Guild if you've got that far. Both of these are on the Social tab and Guild is a tab in your chat window. It's a lot more effective to run a group when you already have people you know from before forming the core.
In the Grouping Tab of the Social window click Create Party.
Look at the quests for the one you want to do and click on it. Clicking on Dungeon will sort them by dungeon alphabetically if you are having trouble finding the quest. Note that it's quest name not dungeon name (eg The Cannith Crystal not Korthos Hall).
Click which difficulty you want: Normal, Hard or Elite. You can't form a party for solo dungeons.
Pick which class you want to see your group. Normally that's all classes but if you have a thing against Barbs or you desperately need a Healer for the last spot you can adjust the filter.
Pick the level range. The level of the highest level player relative to the level of the dungeon will adjust the exp. So for Cannith Crystal which is a level 1 dungeon if I allow 3rd level characters we will get -10% exp for the run. Personally I usually go with a 3 level range from one under the dungeon level to one over. There is no exp penalty for being one level over or under.
"Higher difficulty dungeons count as "higher dungeon level". I think a level 2 dungeon will count as a level 4 on elite, meaning you could be up to level 5 and still not get an exp penalty."
Fill in the comment section but do not put the name of the dungeon. They see the name of the dungeon anyway besides if you go on to a different dungeon afterwards you will have to change it in two places. Use this for things like "slow careful run" or "zerg fast fast fast" ie something that describes how you want to play. N/H/E is sometimes used to indicate you want to run on Normal, then repeat the dungeon on Hard, then repeat the dungeon on Elite.
Click Advertise as Looking for more Players and your group will appear in the Grouping window.
That's it! Your group is now open for business.
One other thing you may choose to do (I know I'll be lynched for saying this) is advertise your group in General chat. It helps it fill up quicker as a lot of people haven't really discovered this LFM tool yet. If you spam though you may actually discourage people who otherwise would have come (and if they squelch you you've lost them forever).
Managing a party
At low levels the only concern in terms of class composition is a healer. You can make do without a tank or a rogue. It's a lot harder to make do on Elite without a healer.
Healing classes are Clerics and Favoured Souls. You can expect them to tell you if they don't want to heal. To a much lesser extent Bards and Paladins can heal but these players generally won't expect to be healing when they join your group.
If you can't find a healer or if your healer bails halfway it's very useful if you can call a hireling Cleric. You can tell her to heal a specific player by targeting that player (F1 - F6) and clicking her heal. You can tell her to rest by targeting a Rest Shrine and clicking her Use Item/Attack button. Try to always keep a hireling Cleric contract in your inventory. There's one available in Korthos and a wide range of different clerics in the Harbor or if you're over level 3 in the Market. They are pretty cheap so I suggest you don't spend Turbine Points on one.
Sometimes there will be conflict in the party. At the end of the day it is your group and if someone's being a pain you can right click their name and choose Remove unless they're inside the dungeon. Reforming the group and re-inviting everyone except the one who's a problem is also an option.
Do not confuse Remove with Promote or they'll be kicking you!
I've done this twice so far. One guy refused to come to the instance at all and insisted we go do some other instance miles away. Another guy died and gave us some huge lecture about how the game suc ks and he's going back to NWN. They were the weakest links - goodbye!
If you have a good run then keep going with the group. If it's a horrible one then try to at least finish then bail.
If you do keep going update the party advertisement in the LFM tool. Not only do you not want people trying to join the instance you finished with an hour ago you want people to jump in to your new group if you're not full.
After a good run ask people who impressed you if you can add them to friends. Or if you're unguilded and you see someone is an officer you might ask them if they are recruiting for their guild.
Credits: a number of people on the DDO boards helped with some excellent constructive criticism:
Lorien the First One