I think the dealer's are the only ones that carry the manuals. You many be able to get a better price buying online than from your local dealer though.
You may be able to download the parts manual (search these forums for parts manual), or places like Coleman Eqiup or Messicks will often email you a parts diagram for what your working on if you request it.
I don't know about the best place to get one, but I highly recommend the WSM (Work Shop Manual). I got mine from my dealer for my B7200 and it covered everything I could come up with on the tractor. It covered the engine as well. I can only assume that it would be the same for your L3400. I paid $77 dollars for mine about 6 years ago and it is several hundred pages long. I got my money's worth out of it when the dealer gave me a rough quote for worst case $3000 for a total engine rebuild and I decieded to dig in and found the problem (loose rocker arm nuts) and only had to replace the rings that got stuck with carbon. Only cost me a couple hundred dollars for rings and new head gasket. All the bolt torques and head tighting pattern is in the WSM as well as all the acceptable tolarances and clearances for most items. I will buy one some day soon for my B2620.