I just started to work on Git. I use windows 7 and has installed msysgit(1.7.8) and Tortoisegit(1.7.6). The repository is created on Linux server which is accessible thru LA
If you need to use a username/password, there is a much simpler solution than the current #2 answer:
Right-click --> Tortoise Git --> Settings --> Git --> Credential --> Choose "Wincred, all Windows users" --> Hit apply
The next time you enter the password for a repo, that password will be automatically saved.
If you're using a repository that requires SSH keys rather than username/password (which it sounds like was OP's original issue), you need to
Right-click --> Tortoise Git --> Settings --> Git --> Remotes. Find your remote (usually 'origin') then load the PuTTY key from step 2.