If you want to use git for pushing under cygwin via help of plink then here is a short guide.

1. Download puttygen.exe and generate key.
2. Download pageant.exe and open the private key you just created.
3. Add public key to right place/send it to someone who takes care of the git.
4. Download plink.exe
5. Open cygwin and use export GIT_SSH=/cygdrive/c/software/putty/plink.exe to make Git use plink as ssh software (change location to reflect your plink.exe location).
6. Use plink to open connection to Git server so that you can save public key of the server (when used with Git plink doesn't take input from keyboard, this is why we need just one connection). For example plink git.somewhere.org and press y to store key in cache.
7. Use Git to do your dirty work. For example git clone git@git.somewhere.org:project-username.git