I climbed through the $5 dollar to $110s very very fast from a br of something like $150 to probably $3,000 to $5,000 when I started the $110s (I think on the smaller side of that but I probably won a little bit right away before playing around a thousand games with a 2-3% ROI).
Some of the things that helped me move up fast:
- Not having to cashout
I own a business so that provided me my own income for my first year (probably longer).  I kept the original $150 on there and didn't cashout until I hit the $110 level I believe.  Probably didn't even cashout for at least 6 months at the $110 level, but my business is seasonal and I wanted some extra cash in January or February of 2008.
- Not being fancy
For some odd reason I wasn't a fancy player coming up.  I tried to make decisions black and white.  This has come to hurt me somewhat at times (mostly when I hit $110 to $220) but in the low stakes playing a simple solid, aggressive valuebet style is probably the best thing you can do.  Getting fancy and finding high variance, possibly negative but perceived slight +EV spots is going to hurt your winrate.
- Not 3betting very often
This is something that a lot of low to mid stakes players do too often.  Against something like 80% of your opponents you should probably just 3bet for value.  This means hands like ATs+, AJo+, 88+ and probably KQs (maybe KQo and KJo).  You can open that up a little bit against certain players, but to be honest most of these guys will get it in so light and bluff their stacks off, it's just not worth building big pots preflop.  So basically, 3betting a lot is going to probably decrease your winrate in the lower stakes games, and since I mostly 3bet for value I think it served me well.
Now, against weaker, tighter players, you can 3bet all sorts of stuff.  but those players aren't so common in the low stakes and a lot of them are winners.
- Not tilting
If I could quantify my tilt into a number, say 100, that represented the total amount of games I've tilted during throughout my career, I feel like 80% or so of those games would have come in the 5 dollar level for me.  Maybe some in the 10s, but I really became comfortable with poker going into the 22 turbos and beyond.
- Comfort
Going along with the last one, I honestly used to have some fears of playing higher than my buyin level when I played the $5s, moved into the $10s then into the $20s.  I ran like shit in the $20s but was still a little weak mentally.  Then I moved down to $11 turbos (thanks for suggestion dboy) where I had basically lost like 50 bucks over 80ish games previously (and hence went back to those regular speeds).  The second time around I started killing turbos and quickly moved into 22s and then 33s.  The 33s is where I started feeling like a good poker player.  I ran at something like 24% ROI for a little over 200 games and then played probably less than 100 $55 turbos before moving into the $110s.  Since then I've been nearly 100% comfortable at any buyin, anytime.  Today, I have no problem playing a $5600 or something if somebody wanted to stake me for whatever I couldn't afford (lol most of that), the buyins or opponent doesn't phase me at all.  This is probably also slightly negative, bc I feel I don't have much competitiveness in me as many other players I talk to do, but it does prevent me from tilting or feeling uncomfortable while playing.
A few other things that I feel are important when trying to get to the high stakes level that I didn't really follow very well:
- Studying the game - I posted a shitload on 2p2, which was good, but I didn't actually review my own HHs very often.
- Make some videos - I only really made some videos once I hit the 110s.  Moving up stakes, it's always good to make some videos and record your thoughts as you play.  You can always look back on them in the future and see where your weaknesses are and see how far you've come (and also you can sometimes see what you used to do so well that may have worked better).  You can also have peers or coaches review the videos for you.
- Get coaching, talk to other players - I did a good job talking with really good players, but I only bought 3 hours of coaching in my life I believe.  I did it probably after playing 500 to 1k games at the $110 level and probably should have bought some coaching after I killed those $33s.  The problem is, when you're running well and playing well you think you're finally getting what you deserve.  When you run bad you feel like you're running unfairly.  So most of the time you get coached you're losing and unconfident and it's even harder to part with your hard earned money as your br is disappearing.  So, I'd suggest to get coaching when you run well, maybe not a lot, but a few HH reviews or an hour or even half hour sweat from a decent coach (make sure it's within your budget, spending 500 dollars an hour on a top caliber player when you play the 5 dollar games is extremely inefficient).  In my experience, the cheapest quality coach for almost any level has been $50 per hour.
Other options are talking to other players (as I mentioned a bit ago).  This works well.  I talked to players like Hokie, Primo, Cwar, Dboy, Wtfnoway, Waidzu, theopendoor and many others when I climbed from 5s to 110s in my first 6-8 months.  We did go over HHs from time to time, but most of it was just talking poker, trading advice on hands, etc.  Looking back at some of my chat logs, it's pretty sad how stubborn I was a lot of the time.  I'm somewhat surprised I've even reached the "high" page on PokerStars with how stubborn and ignorant I have been about my own play over the last two years.  Take my advice on that one, be open to criticism, even if you feel it's "standard" play.  Even people worse than you can find leaks in your game.
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Gotta run now, 4 year anniversary with the lady, can't be hanging out on poker forums all night or it'll cost me long term ;)