Older homes lose heat through the gaps around windows and doors as much as through the glass itself. The fixes here are temporary, removable and inexpensive, which is why they suit renters as well as owners. Each guide starts with fit: your frame finish, your landlord's rules, and whether the window still needs to open.
One honest caveat before you start: sealing drafts changes the bill for whatever fuel heats your home. If you heat with gas or oil, a better-sealed window will not lower your electric bill much. Work out which bill is actually the problem first.