How do we start?

Ask each of your questions here. You may want to do separate posts.
1) computer
2) Telephone
3) House
4) banking
5) Mail
Just for example.
Computer: we use a Verizon air card for our computer connections. Newer plans are restricted to 5 gigs.
Phone: We have Verizon cells that have worked good for us all over the country.
Banking: We have bill payer setup through our bank. We check it a couple times a week to pay credit cards and check our budget.
Mail: Hard thing to do. We have ours picked up by neighbor or daughter. They forward it to a park or location we give them. My brother did not have this ability. He used UPS store. He had them forward mail when he called them and gave location.
House: Have someone check on it. Don't forget to have yard taken care of.
Good luck!

OK, We have hot water heat and of course running water. What steps do I take so the water lines are empty, and I don't need to heat the house

First of all make check lists. What to take and things to do before you leave. Here's our before leaving list:

Mail forwarding
drain pool
New batteries in thermostat
Turn off water
turn off hot water heater
turn off hot water tap under sink
unplug appliances & TVs
stop newspapers
refrigerator empty?
Freezers?
mineral oil in toilets & traps -
Set furnace to 55
unplug garage door opener

One often overlooked item is to check your homeowners policy. Some policies do not cover if house is unoccupied for more than 30 days.

Then I forget about it. Do not have anyone check anything. Being in a townhouse we have neighbors who will correct any exterior issues and I figure anything else I will worry about in the spring!

You should also spend some time in the Fulltiming forum since you'll face many of the same problems.

You came to the right place, and you will get lots of advice. Some of it will even be accurate and useful. You may want to ask several specific questions rather than the shotgun approach. Learn to search the forum, as a lot of your questions have already been covered. A starting point is to plan on visiting more than one place during your first couple of years snowbirding. Florida has lots of tourist things, but is expensive. South Texas is inexpensive, but windy, dirty, and not quite as warm as South Florida. Lots to learn, experience all you can.