The way i look at it is weddings are not supposed to be cheap, though don't have to be incredibly expensive either. It *should* be the best day of the new couples life and one of union.
Do you have a budget you can tell us?

Are you asking about how to get married cheaply or how to have a cheap wedding ceremony?
If it is the former, then it doesn't cost anything to register your marriage at your nearest ward office, and you are free to turn up in yukata if you wish.
If you want a ceremony just for the two of you, then get a friend - preferably a white gaijin who speaks Japanese with a very English accent - to dress up in a fake vicar/priest outfit (available from Tokyu Hands), and do your ceremony in a park somewhere accompanied by suitable bridal music (210 yen CD from Daiso) on a portable CD player. You could even do it on the beach in Odaiba with the Rainbow Bridge behind you. Don't you have any imagination?

Just my 2 yen.

And if you do not speak Japanese at all and only you two will be at the ceremony, I think you'll need someone who acts as an interpreter, not just at the ceremony but for arranging it (reservation etc.) as well.

For other posters, this was where her question started from:
http://www.japan-guide.com/forum/quereadisplay.html?0+6...

Why don't you start with the shrines listed in the webpage in my previous post?

Thx!