There are some good posts above. Stuff Im gonna try!
AS A GENERAL POINT though Id like to tell you how I imprroved my mining effiency for all ore's not just tin.
As a complete Newb I thought building a quarry would be the answer to all my problems, I was wrong. With a quarry of standard size its first toatal yeild came up at something like 14 tin, 40 some Iron Ore, a boatload of silver, 30 odd copper and then a few each of the other ores. Coal was sorted straight back into a generator to aid the process and I got a few rubbies and lots of redstone. Given all the coal, coke and lava cells it took to power it was dissapointing.
Since I had been mining manually for about a few days to get some resources to start building machines I already had mines down to around the Diamond levels. If you have a jetpack you could start in an old quarry. Once I had enough stuff I found that making mining turtles improved the ore collection a huge amount. They need a Diamond pick axe to start with but on the mining turtle its Unbreaking so is well worth the "Expendature".
I go down to diamond level. Around lava lake level so I might get Obsidian too. Then set off a mining turtle at a solid wall with the command "tunnel 100". Throw in some coal then go and do some other stuff. The turtles dont actually get that much ore (Like the quarry). What they do do though is cut huge tunnels for you. After a while I go back to where I set the turtle (or turtles as it is now) off. Then follow the tunnels they made. I then manually collect all the ores that are easy to reach on the walls of the tunnel. This method also uncovers all the caverns and the like it would take an age to find mining manually. Its surprising how many times I set into the tunnel wall, floor or ceiling for say a block of Iron ore or whatever and then find Tin or Diamonds or whatever behind what I originally started mining. Since Im only gettting the ores its much more ecconomical on pickaxes as im not picking through swathes of cobblestone to get at the ores.
After following my mining turtles, at the monent I have 2 at this low level. I go and manually collect the ores they uncover (Still a pain I know but it doesnt take that long). I typically return with 5 or 6 Diamonds. Stacks of Iron Ore and anything from 20 to a stack of tin depending on my luck. Of course there is all the other stuff like lead, silver, copper etc, etc that I usually end up with decent yeilds of.
One tip though. Once the tunnels are getting a bit long and you had everything out of them. Break the turtle with an Iron pick axe. Take it back to the start and move along the wall and set it off again. At first I would just reach the turtle and set it going in the same direction. Eventually I had tunnels that were Incredibly long and just getting to and from my base would take half an hour without including the Mining time.
Ive been mining this way for a few days now and think though its not the easiest it is probably the most ecconomic. Mining turtles are fairly cheap to make, they run well on coal (which they mine and fuel themselves) they dont need charging. The Iron ore I recover more than makes up for the cost of the pickaxes and they dont break or need repairs.