Following are some of the Steps to resolve this error:

1) Check if user has access to the server/database
2) Check if the users passowrd is updated, If so use the latest password.
2) Check if the server name is correct
3) Check if the SQL Server service is running
4) Configure Log On As in services.msc if this error is occuring while connecting to systems across the network. Change the log on account and check if the error is fixed.

Reference : Devi Prasad (sqlserverlearner.com)