Telecommunications in Sheffield

ISPs - Plenty around. You'll find a good selection in the yellow pages. Sheffield has fast internet available so you should have little problem. Most houses have a telephone line with broadband available but I would suggest not using BT's internet service. Bit expensive. There is no problem using the BT telephone line but services from another ISP.

Mobile plans are pretty much UK wide. Vodaphone and Orange are the best two operators. Others claim a better service but reality isn't the same as the adverts.

Long distance calls. I'm assuming you mean to other countries.
Options.
Skype. The internet is easily fast enough for skype and they have some excellent offers. I use it to speak to UK landlines from Indonesia.
Access from your home phone comes in two forms.
Prefix numbers are often pretty good and cheap but, if you don't trust them, there are many phone cards available.
You find the cards on sale in shops run by ethnic minorities. It's a buy and try to find the best one for your choice of country to call. "Black" worked really well for Malaysia.