Fast transport system in Dwarf Fortress

Solution 1:

Unfortunately, machines and dwarf-hastening devices of all sort currently do not exist within Dwarf Fortress.

Short of modding Dwarves to be innately faster, there is no way to increase their speed.

Since you cannot do anything to speed them up, my suggestion would be to make sure nothing slows them down.

Obviously, the shortest distance between two places is a straight line, so make sure they have a direct path. Make sure that the path is clear, and at least two tiles wide, preferably three. Dwarves can pass each other, but it slows them down.
Also make sure there are no distractions. Even if the farms are above ground, a direct underground tunnel might be best, since there is no chance of them spotting random wildlife and running away.
Placing a few small drink stockpiles will allow thirsty dwarves to quench their thirst en-route, rather than stopping halfway there and turning around because they're suddenly parched (I know this was a big problem before, I can't remember if it's been tweaked since.)
Lastly, tired or injured dwarves do move slower than others. Make sure your dwarves are well rested and taken care of.

If you're looking to simply speed up the process of farming, there are some additional steps you can take.

Assign your growers to burrows there. Build some little rooms for them. Put in some beds and tables. If they don't have to walk back and forth very often, the entire process will speed up. Put a few small food/drink stockpiles there to be filled for them. But if you do this be sure you...
...Micro-manage your haulers. If you have the dwarfpower, assign a few dwarves to do nothing but carry food from the farms to the kitchens and seeds the other direction. They'll do so very efficiently, because they won't be wasting time walking between many different areas of the fortress to haul goods between.
If too many dwarves are wasting time walking to the farm to pick a plant, turn the option off in the orders menu; this way, only your planters (who are already there, since you followed step one) will pick plants. You may need to assign another planter, tho, to handle the increased workload.

If you are talking about moving stone, you can use catapults to do so. It is detailed in the wiki. But not food unfortunately.

I think the best solution would be cover the old farms in lava, and then build new farms closer to your fortress.