To try to clarify things a bit:
1. Using ANY iPad WITHOUT the need for any additional equipment and WITHOUT paying for anything:
a) You can connect to free wi-fi in independent pubs, cafés, etc in the same way that you connect to your home wifi. (i.e. locate the signal, click 'Connect' and enter the password provided by the café owner, etc)
b) You can connect to free wi-fi in chain pubs (e.g.Wetherspoons) , supermarkets (Tesco, Asda, et al), etc in a slightly different way. You normally 'connect' as before but there's no password. Instead you have to try accessing any website (such as the BBC or AB) and you'll find that you're initially redirected to a registration/log-in page for the particular service which you're using. After getting past that you can browse normally. (The method varies slightly between providers. Asda requires you to register, receive a pass code via a text on your mobile phone and then enter that on screen).
c) If you're a BT broadband user you can connect to any other BT customer's Home Hub (using a completely separate, entirely secure connection) free of charge. That means that you can find free wi-fi almost anywhere. (The connection method is similar to (b) above, requiring you to go via a log-in page). [It's also possible for non-BT users to pay to access their system but, unless they only require very limited usage, it can be quite expensive]
2. 'Base model' iPads only work with wi-fi. You can't connect them to the phone network. However the more expensive models allow you to insert a data SIM, so that you can use the 3G or (far faster) 4G phone systems. Just like using a mobile phone's SIM, you need to pay for your data usage.
3. The 3G and 4G dongles which work with laptops won't work with iPads (because they require the Windows operating system to be present). However you can get around that by using a Mobile Wi-fi device, which connects to the internet over the phone network and then works in much the same way that your home router does. (Once again, you need to pay for your data usage).