How to check for air in heating and cooling system

They have a tool called an "Airlift" that puts the system under a vacuum and then draws the coolant in without air.

http://www.tooltopia.com/search.aspx?find=airlift

Is there something less expensive or another way?

Sure, you could take it to a shop and let them do it. They make these tools for a reason. It is very difficult to get air out of some of these systems do to the design. Some cars it will just work itself out by driving and topping off when cold. There is also the possibility that a previous overheating has caused head gasket damage and that will continue to release combustion gasses into the cooling system faster than you can take the air out.

It is not over heating it is just not blowing very hot heat and the antifreeze in the radiator is always cold no matter how long it has ran, but the heater hose's are hot and the upper radiator hose is hot.

If both heater hoses are hot, then you are barking up the wrong tree. You need to be looking at the air blend doors in the dash to see if they are working.

They work, but why is the antifreeze cold in the radiator and there is no pressure when I take the cap off?

Because the radiator is doing exactly what it was designed to do. You might want to check the actual engine temperature in the computer to make sure your thermostat is not stuck open or is using the incorrect temperature stat.

Something else is wrong because the upper radiator hose gets very hard also if you squeeze it.

Well, I disagree.