When outputting a single user, you can simply define what user you want to place data from. You can do this by using the title, alias or id of the user:
{user name="Peter van Westen"}...{/user}
{user username="peter"}...{/user}
{user id="123"}...{/user}
When inserting the {user} using the id attribute, you can also add a comment (eg. the Title) after the ID with the following syntax. For example:
{user id="123#This is Peter's ID"}...{/user}
This last syntax, unlike when using just the title attribute, won't bind the user to always keep the same title, because the syntax will still only depend on the ID. However, this allows you to add a comment to remember what the user is about when you insert it.
Current User
You can also make the tag use the current active user.
To do this, simply don't give the user tag a specific user:
Welcome {user}[name]{/user},