Amazingly, this is the first I've heard of fx/tx/Fx. How ridiculously awesome.
document.getElementById('asweetid')
and you want to grab just the id for use elsewhere. In command mode pressing f' will move your cursor to the quote, yf' will put 'asweetid' into your yank register and a p anywhere else will paste it. I also make heavy use of ctx where x is a character on a line that I want to replace up to. The best part about vim, I think, is how I think about the commands in my head and they just kind of flow out of my fingers.
"Hmm I want to change (press c) to (press t) that closing paren (press shift 0)."
Even just typing that my left hand instinctively moved toward the caps lock to go to command mode.
It's helped me polish off those last few vim commands that I never got used to. I recommend looking at it daily.
That's the tutorial that fed me that chart in easy-to-manage pieces, easing me into vim nicely.
Also highly recommended, the rant by the same guy: http://www.viemu.com/a-why-vi-vim.html