A marriage is an oral contract, you must declare you are free to marry one another, and contract to take the other person in marriage. Signing the register is a record of your marriage.
The legal words
You must make the legal declation in the words laid down by law. The choices are;
THE DECLARATION
1. I do solemnly declare that I know not of any lawful impediment why I .............. may not be joined in matrimony to .............
2. I declare that I know of no legal reason why I ........may not be joined in marriage to ............
3. By answering "I am" to the following question "Are you ............. free lawfully to marry ...............
THE CONTRACTING WORDS
1. I call upon these persons here present to witness that I .......... do take thee ............... to be my lawful wedded wife/husband
2. I ............ take you ............... to be my wedded wife/husband
3. I .......... take thee ........... to be my wedded husband/wife