World of Warcraft is a multiplayer game for a reason--you CANNOT run the entire game by yourself. While there is a lot to experience on your own, solo play is not the focus and a lot of experiences in the game simply cannot be had without a group. One of the easiest ways to have a convenient and reliable group is to get some friends together and form a guild.
Think of what you want to do. Are you a high level character that wants to go on big raids? Are you a low level character that wants to get higher but needs help? Do you just want to enjoy the game with your friends? Your goals will greatly affect what type of guild you form.
Bring a friend. If you know people from real life or have made friends online, ask them if they have a guild already. If they do, ask them if they'd mind helping you out. If not, mention that you have an idea for a new guild. You need 10 people to form a guild.
Think of a name. A good name can make or break a guild. If you idea is to just have fun, consider some fun or humorous names. If you are a hard core raiding or leveling guild, maybe something noble or intimidating will work better. A lot of people may or may not sign your charter when they hear your idea for a guild name.
Be democratic. Consult all your possible recruits regarding the guild name before making it the official name-to-be. If necessary, have everyone cast votes on a list of names.
Go to the Visitor's Center in any major city and look for the Guild Master.
Purchase a Guild Charter for 10 silver.
Find 10 people to sign your charter. If you don't know people, advertise on the Guild Recruitment channel. Lots of people are looking for guilds, some of whom are willing to gamble on a new one.
Bribe if you have to. If you are experiencing difficulty getting people to sign your charter, consider a small honorarium for those that sign. A few silver will usually help change some minds. Don't give out too much.
Chat with people. Aside from the Guild Recruitment Channel, people are most commonly found near the bank and auction house. Talk to them, strike up a conversation. Do not immediately start out with "Hey, you wanna sign my guild charter?" Nobody likes a forceful guild merchant. Ask them what they're interested in, what they want in a guild and if it looks like they might enjoy what you have to offer, ask them if they'd like to sign.
Remember that everyone who signs your guild charter will immediately be placed in your guild as soon as the charter is ratified. They need not stay in the guild once your guild is created, but the expectation is usually that they will stick around for at least a little while (unless you just bribed 10 people to sign, in which case you may shortly enjoy a single-person guild.)
Get it registered. Once you have 10 signatures, take your signed charter back to the Guild Master to get it official. Once it is official, your guild is created. For some reason, your guild charter must be in your main backpack in order for it to be recognized by the Guild Master. If you have the charter stashed in a side bag, it will not be registered.
Your guild is now official! Now is the time to thank everyone for signing and to get down to the business of appointing officers to aid your members, deciding who will perform what duties, designing a tabard and getting the word out to possible recruits.