First, have a look at your window. You can usually see where caulk has broken, which will show a crack or gap. Inside, you can check the sealing around your windows to look for any cracks or breaks in the putty that joins your single-pane windows to your window frames.
Lightweight curtains will also show a draught. If you shut everything that leads to your room and switch off anything that might move air, lightweight curtains may move. If they start swaying, this is probably due to air getting through the windows.