Determine what headset bearing size The headset bearings are going out in my bike.  How do I determine what I need to order.  See pictures that might be helpful.

The Bike is an older Trek 3700.

Thanks,
Paul
That size looks like an EC34 (external cups, 34mm inner head tube diameter for forks with 1.125 inch steerer tubes).

You'll either have loose balls, balls with a retaining cage (metal or plastic), or cartridge bearings.

If you have caged bearings, loose bearings will work fine but be more fiddly to install. Take one to your LBS or hardware store.

If you have cartridge bearings, the size will be moulded into one of the rubber seals or be laser-etched on the side of the casing. Your LBS may stock one or two common sizes if you're lucky. Otherwise either buy a complete headset which uses the same size, or buy a complete headset and get it fitted or press it in yourself. Complete headsets can be cheaper than replacement bearings but the cost of paying a mechanic to install it will exceed the part cost.

TH Industries make the bearings used in many headsets. Their brand FSA offers a variety of affordable good quality headsets.