Neverbeenabroad - go for it! I applaud your desire to spread your wings. It might seem intimidating, but it doesn't have to be.
Where do you want to go?
1st, get a passport. It isn't difficult, Google UK passport office, applying for a passport and follow the instructions. If you want extra help, pop along to a Post Office and they can walk you through the process.
Regarding visas, it all depends on where you are going. If you are a UK national then you will be able to travel to countries in Europe without a visa. For countries outside Europe the visa regulations differ country to country. Again, have a look at the FCO (Foreign and Commonwealth Office) website and search for visa regs by the country you want to visit.
Money: again depends on the country. Most places in Europe and the majority of developed countries you will be able to withdraw local money from their cash points just like you'd do at hope. But be aware that you will incur a charge for doing this. If you'd prefer to have some cash in your pocket before you go you can buy foreign currency at the UK, again the Post Office or your bank is a good starting point. I'd say that having a little bit of the currency when you arrive is always a good idea.
Plane seats - depends on the airline. Most budget airlines (EasyJet etc) will not assign you a seat if you buy the cheapest tickets, you just have to pick one when you get onboard. Although you can usually pay extra to chose a seat. Most other traditional airlines, such as BA, will assign you a seat when they issue the ticket.
As for the process - enjoy it! Pick where you want to go depending on the sort of trip you fancy (sun, culture, adventure etc) - and do some reading around the place. Work out eh best time of year (do you like the heat or the snow?) and start looking at flights.
This can all be done using Google as your friend. But if you want some extra help, why not go to a high street travel agent and sit with them as they talk you through it. They can show you what is possible for your budget and advise you on your options.
Talk to your friend, where have they enjoyed going? Most people will love to talk about their travels!
Sorry - massive question and I could write essays here. If you want any more specific advice just shout.