Many MMORPGs that offer Player-vs-Player action also offer some type of cross-race, cross-class grouping to occur, usually in the name of Clans, or in World of Warcraft's case, Guilds.
What Is A Guild For?
Guilds are meant to give an individual a "family" to socialize, quest and adventure with. Guilds have chat lines that all Guild members can see and participate on, and it's a great place to meet others who play at the same time as you do regularly.
Guilds are not all benefit for the member, however - at times Guilds or Clans can be deemed to be "at war" with one another and it is your duty as a member of the Guild to avenge Guildmate's deaths to other Guilds or participate in other retalitory actions determined by the Guild leader.
Some guilds will require you to make financial donations, or equipment offerings. Beware, as this is not a standard expectation in all guilds.
Unfortunately, Guilds don't have guild halls, fellow guild members aren't easy to make out when they walk past you on the street, and there's no real "common hanging out area" for guildmates. Your connection to your guild mates is primarily through chat.
How Can I Tell It's A Good Guild?
Even if you're a solo player, you need access to people who can team up with you to go through particularly difficult quests or dungeon instances, etc. Guilds are a great way to find these people, as you get to know your guildmates over time and therefore your parties are more reliable and you'll have less "people problems".
You can't tell if a guild is a good one from the outside, really. The only way is to join and give it a whirl yourself.
"Trying Out" A Guild
Be prepared to stay with this guild for a couple of weeks to really get a feel for whether it's for you or not. It won't hurt you to stay in the guild... there's no restrictions for leaving and joining other guilds and there are plenty to join at any time.
Chat on the guild line. Ask questions, answer questions. Read what others write, and think about it. Offer yourself when someone asks for volunteers to do specific quests or dungeon instances and you're within 5-10 lvls of them. Get involved in "team" things now and then.
After a couple of weeks, you can easily decide whether this Guild fits your needs and personality or not.
Where To Get Guild Invites
There are a couple places you can get invited into guilds from.
Friends are a great place to start - if you have someone you've already teamed up with and have on your friends list, ask them if they're in a guild and if you can get invited.
Listen to the General chatline that you're subscribed to automatically when you first login. Regularly there are people starting new guilds and looking for the first round of members.
I'm sure you could also sit in some town and talk to each person who comes around who's in a guild and ask them if you could get an invite to their guild as well. Not my choice really, but hey, I'm sure it would work if you said it right and found the right person.
Leaving A Guild
Just so you know, if you go into your /who menu and then into guild, and right-click your name on the list, you can "Leave Guild". I had a bit of trouble finding that myself when I was leaving my first guild.
You can also use the text command /gquit to leave your guild.
It's not a big deal to leave guilds. If you met some people you want to keep in touch with, put them on your friends list and make an effort. Otherwise, leave the guild and go on your way, and find another guild if you left because of a "bad fit" with the last one.
If anyone harasses you about it, the /ignore command works really well :)