GENUKI have a great guide to getting started, so I'll just give my quick thoughts and I'll come back and update this as ideas occur to me. It's a personal guide and one aimed at building your family tree at minimal cost (because I'm cheap).
Anyway, as they say - the best time to start was yesterday, the second best time is right now. I found this out to my cost when I took my great aunt a bit of a questionnaire to try and winkle out all the information she had and she had a massive stroke minutes before I could hand it over. She never recovered and a lot of vital information and contacts were lost. So start asking your oldest family members for information asap, not just dates and locations but any stories they may have been told - I've confirmed a lot through the paperwork.
Right, now you have a bit of information, where can you start putting it together? Answer: The Mormons. Some people might be a bit iffy about this but they are a leading source of genealogical information and they have the transcripts of a lot of key documents. They also have a handy family tree builder that integrates very nicely with their information - you can attach sources to your tree and add to your tree from sources (especially census returns). When you get back to the 1911 census things really start motoring. It's a shared tree so you will bump into research other people have done and it's worth double-checking their work.
As I say, they largely have transcripts but you'll want the originals - with some variation, most scans of original documents can be found on Ancestry.co.uk and FindMyPast. If you have a solid enough tree and plenty of questions, then they both have a free trial period that I definitely recommend grabbing and cancelling when you have strip-mined what you can. You will have further queries, so keep notes and when you need answers, pop to your local library - they should have a subscription to one or both. You usually get an hour so use it wisely and email the document scans they have to yourself for future reference.
What the big geneaology sites have can only get you so far, so it's time to summon some paperwork. And, yes, this bit costs but it's not excessive. You should have stumbled across the birth, marriage and deaths index by now but if not, check it out at FreeBMD. These will help you confirm years (where census dates are approximate) and it gives you what you need to order the relevant certificates from the General Records Office. You can get the paper copy but they also do research scans (it was births and deaths last I checked) that they email to you, which can work out quite a bit cheaper. Note: it's not just good for getting the certificates as the GRO has expanded the index to include mother's maiden names back before this was a part of the index.
Unless you've run into multiple brick walls you should have some branches back to the 1800s. So I would recommend putting your tree on Geni.com - it's another shared tree but is much more visible and useful for collaborative research. You can also get most of the value out of it without paying.
And those brick walls? I've found the best place is the RootsChat forums, specifically their lookup requests sub-forums if you drill down by county. Don't expect them to do the basics (everything above) but if you have exhausted all other avenues, post what you know over there and see what they can do - they've broken through two for me.
Right, that'll do for now. If you have any questions about what I've said or tips for helping people get started, then throw them in. If you need help with your research then start a new thread.