Try a quantum stockpile first.
1. Set everything up, before you get anywhere near the hauling menu. You don't necessarily have to do things in the given order.
a. Make a minecart.
b. Build a track stop, set to dump north.
c. Make a 1x1 stockpile, one tile north of the track stop. Set it to accept from links only, and enable the whole category of whatever it is you want stockpiled (no need to be specific here).
d. Make a larger stockpile, close to the track stop and 1x1 stockpile. Set it to accept from either anywhere or from your desired workshop(s), and enable only the exact items you want stockpiled (this is why you can be non-specific with the minecart and 1x1 stockpile). Set the number of barrels and bins to zero.
2. Now that you have your feeder stockpile, your dump stop, your quantum stockpile, and your minecart, you need to tell the dwarves how to use them. Again, the given order is not necessarily fixed.
a. Enter the hauling menu.
b. Move the cursor over the track stop.
c. Press r to make a new route, press s to make a new stop where the cursor is.
d. Press Enter to start defining the stop. There are a lot of options here, but a quantum stockpile setup needs few of them.
e. Stops are created with a few default depart conditions. You don't need these for a stockpile; press x to delete them all.
f. Press Enter to tell the stop* which items it can take. Select the whole category of whatever it is you want stockpiled (the feeder stockpile has already done the job of item selection).
g. Press Escape to return to the 'define stop' screen, and move the cursor over the feeder stockpile and press s. This links the stop* to a stockpile, linked stockpiles being the only ones a stop* will consider when looking for items.
h. Press Escape to return to the hauling screen. This screen is the one in which minecarts are assigned to routes. The stop you were just defining will be highlighted, so press v to assign a minecart of your choice.
i. Press Escape to return to the main game.
3. Now, just wait for the dwarves to do their thing. They should be taking stuff to the feeder stockpile, with one dwarf going to place the minecart. Before the minecart is placed, going into the hauling screen should show a red V by the route's single stop. This means that the assigned vehicle isn't at the stop it should be. Once the vehicle is placed, the V should go green and dwarves should start moving stuff from the feeder stockpile to the cart.
*Any "stop" with a * after it is interchangeable with "minecart" in this particular case. There's only one stop and the minecart never moves from it, so the minecart and the track stop are not wholly distinct. They're not the same thing though -- it's the stop that loads or unloads items, despite the "Items Desired/Kept By Vehicle" text.
I'll point out for the sake of completeness that you don't have to pick north as your direction: I just wanted to write as few words as possible in the instructions. You also don't have to do everything in the hauling menu all at once, since it's pretty independant in its function, but if you don't have the stockpiles and minecart ready you'll have to exit the hauling menu and come back once you have those things ready. Easier to have a fixed list of steps, which makes it easier to spot booboos like forgetting to say which items will be put in the minecart.