You don't have to adventure alone in World of Warcraft. In fact, the game can be more fun when you join with other players. Quests that are too difficult alone can be surprisingly easy to accomplish when you group with other players. If you group with other players frequently enough, they might even become regular adventuring companions and friends.
Creating a Group
A group, or party, of adventurers can have a maximum of five players. A group is created as soon as one other player joins you. You can invite a player to join your group in three ways.

You can select the player, right-click on the player's portrait, and select the invite command from the resulting dropdown menu.
You can type the /invite command followed by the player's name at your chat prompt.
You can add the player to your friends list, then select that player from your friends list in the Social window and click the Group Invite button.
Players you can see next to you can be invited by any of these three means. However, players that you cannot see, usually because they are far away or in a different zone, must be invited through the /invite command or through the Group Invite button on the friends list.
A player already in another group cannot join your group. If you extend an invitation to such a player, you will get a message back saying the other person is already in a group.

Joining a Group
If you are adventuring by yourself and are invited into a group, you can accept or decline the invitation. However, if you are already in a group, then you will be unable to join a new group until you leave your current group.

Switch to Party Chat
Type "/p text" to switch to party chat. This allows you to communicate only with members of your party.

Group Leader Options
Type "/kick playername" to remove a player from the party. You can also right-click on their name and select "uninvite".

Leaving a Party
Right-click on your player portrait in the top left corner. Select the option to leave the party.

Party Member Options
Select a party member's portrait and right-click on it to see what options are available to you. Some options are only available to the group leader, or only when the party members are next to each other, such as trading and inspecting.

Locating Party Members
The minimap shows little green dots or arrows showing where to find specific party members. Place your mouse over the dots or arrows to see who is who.

You can also check which area party members are located in by mousing over their information box on the left side of the screen.