How can I set permissions for a user to only see one project?

[Vasiliy Zverev]

Yes, it is possible.

How to do this depeneds on how many projects use this permission scheme.

If it is the only project then you can just add this user to browse permission.

If there are more than one project then it is better to create/use existing project role into permission scheme. 

Add user to role only for project you need.

[Joe Pitt]

JIRA works on the grant permission model. You need to only grant them permission in the one project. Many people start off by granting the jira-users group permission. That gives permission to anyone that can logon. I believe the best model is to use project roles and grant permission by role in the permission scheme. Then the project admin can add/delete users as desired from the roles. It has the advantage of taking the JIRA admin out of the loop of giving users permissions. There may be a few projects where you really want everyone who can logon to have access, but in my experience those cases are few.