Electrical staples.

Best situation is that you have carpet, and are able to pull it up an unnoticeable amount along the edge, and staple into the subfloor where no one will step on it. Next best is to staple into the baseboards as close to the carpet as you can get, then fill in the holes (if they're even noticeable) when you move out.

Unless, of course, you're super lucky and there's room to just tuck it under the baseboards - which is what I ended up doing in my office. Nothing to see, nothing to secure, nothing to clean up.