Firstly create your user login at the instance-level and map the user to the database you want access to.

Secondly, from the Security tab of the database, assign the user the correct rights and permissions and accessibility should be assured!

If it isn't then I suggest checking your collation to ensure that, if your collation is Case Sensitive (CS) and not Case-Insensitive (CI) that you have typed your database exactly as presented.