Is it just a mobile you have ?
If so you won't necessarily have a router.
The mobile should be set up to allow data access via the talktalk network (Vodafone I believe). In which case you need to switch data on in the mobile settings and start to pay for data (or use up whatever allowance you have).
WiFi is a different way to connect to the net and then it goes through a router. But you must either have your router in signal distance, in which case you should know it's password, or you need to find a free WiFi somewhere public which may or may not need a password. If you do then the cafe, pub, or whatever would probably give you one; or maybe you can to give details such as an e-mail account to get free access. Whatever.