How hard is it to move washer/dryer from an upstairs room to the basement? What hookups would we need, etc?
Chris is right, but let me add. You really want BOTH and hot and cold water feed. If you leave off the hot water and don't cap the input, cold water may escape out the hot water feed port through the mix valve (if so equipped) when the machine is set to warm. Besides, your wife will be upset when she tries to bleach whites with no hot water!! You will need to install a drain with a trap for the waste water to pump into. As long as you have a drain line close by to tap into that is not more than a couple of feet higher than the top of the washer, you can use that. The machines today can usually raise water a couple of feet above the machine, but not much more than that. You will need to install a 15 amp, 120 VAC line with receptacle for the washer and a 30 amp, 220 VAC dryer outlet connected directly to your breaker box equipped with the matching double pole 30amp breaker. Last is the dryer vent to the outdoors. BTW, years ago my wife made me take the washer/dryer out of the basement and install them in a utility closet on the second floor closer to the bedrooms. No more lugging laundry up and down stairs.
You need water and power going in and drainage/air vent going out.
If the washer is just cold fill, or can be used as just cold fill, then you just need cold water. If not you'll need to run a (properly insulated) hot pipe down there too. If the washer has a hot water inlet you'll need to connect that to the cold fill too - you can get a Y connector to split the cold feed into two.
The drainage might be a problem. You'll need to check that the drains are lower than the basement floor. Otherwise your waste water won't have anywhere to go.
The exhaust vent for the dryer shouldn't be a problem as you can run the pipe upwards if necessary to an outside wall. You might have to buy a new/extension for it though.