1) Watch how you get around:
This may sound obvious, but for someone who didn't do any research about London, it would be easy to spend vast amounts of money on transportation. First of all, in the center of London, most stuff is within walking distance. When looking on the map, you may think, 'wow, that's 6 stations away! I don't think I can walk it!' But, be careful to look at the actual distance. You may be surprised how close it is. On my first day, I only took the metro once and on the second day I took it twice. On the third day though, in order to save some time, we took the metro and bus a little more often. As far as getting metro and bus tickets to get around, be sure to get an Oyster card. This little card will make your trips around London much cheaper, and you don't need to go up to the machine every time you want to get a ticket. Don't forget to cash out your Oyster card when you leave. You'll also get back the £5 deposit you made on the card when you leave the country.
Another problem I encountered when I wanted to go to Brighton (1 hour south of London by train) was that tickets were really expencive. £29 for a round trip ticket seemed a little steep, but I figured, I would have spent the same on a hostel if I stayed in the city so I just paid it. Then when I went to Brighton, it turns out my friend there knew a website where he could buy a round trip ticket to from Brighton to London that included a subway pass for the entire day for about £12. Of course, tickets like these can't be purchased by just any tourist, you need a British credit card to buy them. But, if you know some locals, you could theoretically get them too. Their use is not restricted to British citizens only, just the purchase. Make sure you ask your friends to look for discounts that you can use too!
This may seem like an obvious one, but you should avoid taking taxis. Traffic in downtown London is quite terrible. Our Big Bus tour guide joked that the speed of traffic in London hasn't changed for the last three centuries, the speed of traffic is no faster now than when people got around by horse and buggy. The minimum cab fare is £2.20 ($3.60) but goes up quickly and for going one mile, you should expect to pay £5.20 ($8.50) as a minimum, but could be much higher if you are stuck in traffic.
2) Watch where you eat:
If you go to many restaurants in central London, you may think that eating out in London costs a fortune. That's probably because you've found yourself at one of the thousands of restaurants that cater to tourists. It's not unreasonable to say that 2/3 of the people you'll pass in central London on a summer day will be folks on holiday, so there are plenty of places set up to rip these people off. It's best to look around and see where the locals are eating their lunches. I'll certainly bet it's not one of those traditional looking English Pubs. Here are some suggestions for where to get a cheap bite to eat:
Supermarket lunch
Matt's homemade bread with cheese and meat which we ate next to the Themes
Curry at a take-away place
Cheap pints of beer at Wetherspoon
Gourmet pizza and cheap beer
Fish and chips in Brighton, bigger and cheaper than in London
3) Go local!As I alluded to before when talking about train tickets, getting a local to help you get around is definitely a plus. While I tried to couchsurf while I was here, I was unsuccessful finding someone to host me from the website. But, as it turns out, we were hosted on Saturday and Sunday night by my friend's sister's roomates, and it turns out they are couchsurfer hosts too! Staying with locals, either friends or couchsurfers has two great benefits. One is that... well, it's free. But two is that they can show you the good, local places to go or give you insider tips on how to do things cheaper, like, for instance, the cheap train tickets. While we were in Brighton, my friend was also able to get half priced admission for himself to get into Brighton Pavilion and so we just split the total cost so it was cheaper overall.
Brighton Pavilion
The cloisters of Westminster Abbey (admission free)
London has lots and lots of things to do for free. For lists, you can just google 'London for free' and you'll get millions. Many churches, museums, markets, and sights don't cost a thing. We went to four museums for free; the British Museum, the Natural History Museum, the Science Museum and the Victoria and Albert Museum. Another little thing we realized was that to go into Westminster Abbey and St. Paul's Cathedral was £16 and £14.50 respectively. But, to go in as a worshiper during their services for free. Granted, you don't have the same experiences or photo opportunities, but it's quite impressive to tell your friends at home that you went to Sunday services at Westminster Abbey and sat how many feet away from where William and Kate were married? Or attending Evensong in the evenings at St. Paul's and say you listened to their choir in those enormous halls. Don't forget too, that the cloisters and St. Margaret's Church on either side of Westminster Abbey are always free and open to the public.
Giant sloth in the Natural History Museum
Real moving steam engine at the Science Museum
Hanbok made from bojagi at the Victoria and Albert Museum
Egyptian statue in the British Museum, (aka the museum of cool, stolen things)
Changing of the guard starting from St. James' Palace (we had a great view here, those who went to Buckingham Palace couldn't see a thing)
Evensong at St. Paul's Cathedral