To connect a local drive to your remote desktop session, first select "Show Options" on the new connection window...
Next, select the Local Resources tab and click the More button at the bottom...
Select the drive you want to map, for example your local C:\ drive...
Press okay, then connect as normal. Once connected, if you open up the Windows File Explorer, then on the left pane, select Network, tsclient and then you'll see your local drive, where you can save files for you to access on your local machine, or load files up onto the remote server...