As suggested by ABerrant, I'd recommend that you DON'T use vinegar, windolene or other such products.
I'm a window cleaner and I can tell when a customer has attempted to clean their windows with a product such as this, as it leaves a residue on the windows. They might look nice and clean, but I can tell when I'm cleaning them, that there's some kind of residue on there - it takes me longer than normal to clean the window.
Find out from your window cleaner where he gets his window cleaning supplies from and go and treat yourself to a decent squeegee. Don't be tempted by the ones for a quid, they're useless - a decent squeegee will cost anything from a tenner upwards.
Use soapy water (the same strength that you'd use for washing the dishes) and apply sparingly onto the windows with a cloth or sponge. Get your squeegee and squeegee the water off from side to side. Don't try anything fancy - just go from side to side. When you reach the other side, dry your squeegee with a dry cloth and then squeegee again, further down the window from side to side, working your way down the window.
If you have a window cleaner, have you tried asking him if he'd clean inside?? I clean inside for some people ..... I'm easily bribed with the offer of a brew and biscuits, on top of the extra few quid that I'd charge for cleaning inside :P