Electric dryers probably have a diagram showing how to wire for 120V.
The motor and timer are between one hot wire and neutral. You just hook the other hot wire to neutral.
Try one of the hots. If that doesn't work, try the other instead.
Older dryers used a 3-prong plug for 240V, and ground and neutral shorted together.
If newer with a 4-prong plug, neutral and ground should already be separate.
Dryers typically come without the cord, and you buy a 3-prong or 4-prong plug & cord depending on which outlet your house has.
Best to have ground separate, properly grounded. I changed my 3-prong to 4-prong so I could use a GFCI outlet.
Water heater, if just a resistance heater with mechanical thermostat, you just wire to 120V (hot and neutral) instead of 240V (L1 hot and L2 hot). It draws 1/4 as much power, still achieves same temperature but takes four times as long.
There are a bunch of these 120V AC conversions on youtube. Not that hard. A friend modified one to work off his solar array. When he turns on the dryer it diverts solar array power which would go to his water heater to the dryers heater element. I once had a heater element burn out. I grabbed a new replacement element that I got at an auction. Evidently it was low power and wife said timer ran out before clothes were dry. I could have shortened it but put a 5min on/off timer in series with existing timer to double the rated time. Just be aware it will take much much longer. So you better have electronic control which senses moisture.