I'm an apartment-dweller, and I managed to inherit a washing machine and dryer (no more collecting quarters and trips to the laundromat--yay!). But there are no hookups in my apartment (boo!). This is my solution to this problem.
Note that I never signed anything in my lease forbidding me to have a washing machine--you might want to check your own lease for details. Also, my downstairs neighbors are cool with their dishes rattling when I do laundry.
Step 1: Extension Hoses
None of the hoses that came with the washer are long enough to reach the sink. The supply hose is female hose fitting (both ends)--I just cobbled one together out of plastic hose repair fittings and clear braided tubing (all available from Home Depot).
I extended the drain hose with 1-1/4" ID braided tubing--it is a friction fit around the outside of the drain hose (see the second photo). I secured it with a hose clamp. This works fine with a corrugated drain hose; I'm not sure how well it would work with a smooth surfaced hose.
Step 2: Sink Connection
Another piece you need from Home Depot: a sink aerator thread to hose connection adapter (piece at left on photo; aerator at right). It's sold in the rack of small plumbing fittings (along with washers, sink replacement parts, etc).
I've found that hand-tightening the adaptor is about right--overtightening with a set of ChannelLocks makes the rubber washer squeeze out of its correct shape, causing a leak.
Adaptor gets connected to the faucet. Hose gets connected to the adaptor. Knee bone connected to the shin bone.
Step 3: Connection to the Washing Machine
The supply hose needs to be connected to the cold hose connection. You are going to be controlling water temperature with the faucet controls (hot/cold/warm). Since the rinse cycle is usually cold, you need to hook up to this side to make it work.
Note the hose cap on the unused hot side. This is actually important. The solenoid valves have enough slop in them that there is some leakage out of this connection, even when you're just running the machine on cold. Yeah, I found this out the hard way.
Step 4: Finishing Setup
You might notice the velcro ties holding the hose together (like this). I considered it good insurance, to keep the drain hose from flopping out of the sink mid-cycle.
Make sure all the connections are tight; turn on the water to the temperature you want it. Fire it up, and do your laundry!
Note that if you wanted to do a cold rinse, you will have to change the faucet settings mid-cycle.
Step 5: Wrap-up
When you disassemble the hoses, be sure you have a bucket around to drain them out.
Step 6: Wrap-up, Part Ii
The second use for the velcro ties is to keep the hoses in place, when the machine is not in use.
Yay! Clean underwear!