I don't know about recording to an external drive, but there is no recording option I could find except setting up an Extender on your network. What you probably need to do is change the quality of the recordings. The default might be set to Better or Best which takes up huge amounts of disk space. Set it to Good. I've found that is perfectly adequate for tv shows. I've never tried Fair setting. You can manually move the recordings to your external drive to save and free up space. Your other option is to install a bigger drive. Low disk space affects everything you do with the computer, not just recording. Doing a disk cleanup might help if your drive is big and clogged with old recordings and unused programs and files.

This can be configured in Media Center, under Tasks -> Settings -> TV -> Recorder

 

The location for recorded data is under Recorder Storage.

The retention policy is under Recording Defaults (and the as-shipped setting is 'keep until space needed').