Go with extra bedsheets or newspaper when you need privacy that first night or two. Mount sheets carefully, trying to hide thumbtack holes or pinholes; tape newspapers directly to the window glass and clean up gummy residue with a razor blade scraper.
Add a decorator touch to the basic blinds, shades or other window coverings that may be provided by the landlord. A lightweight, ready-made valance can put a spark of color in the room; you can hang it on a basic curtain rod with four screw holes that are easily patched with Spackle at move-out time.
Go with an inexpensive roller shade for both privacy and a thermal block if the windows are uncovered and/or leaky (take the shades and mounts with you when you move; most can be cut down and reused). Roller shades can mount inside or outside the window depending on the situation; you'll need to fill a few screw holes when you move out.
Use a spring-tension rod to hang curtains inside the window frame. These reusable, adjustable-width rods cause no damage and can support a lightweight curtain or valance.
Hang flat sheets (new, unwashed ones are best) by running rods through the opening at the top of the sheet. Add a ribbon tieback and the look can be quite fetching.