1. If there is a ground wire available in the box, it will probably be bare uninsulated copper, or have green insulation, solid green or green with a yellow stripe. If the wiring is run in metallic conduit to a metal box, the box itself may give you the ground you need.

2. You can't connect to the ground for another branch circuit, but for a retrofit like this you may be able to run a ground wire to the ground rod or other grounding electrode, or the wire attached to the ground rod (grounding electrode conductor).

There is usually a grounding jumper in the dryer that you can install with a three wire cord. This provides protection in the event of a wiring fault without changing your wiring. Unless you're 100% sure you've got a good ground, it might be better to just set up the dryer for a three wire power connection.

1. If there is a ground wire available in the box, it will probably be bare uninsulated copper, or have green insulation, solid green or green with a yellow stripe. If the wiring is run in metallic conduit to a metal box, the box itself may give you the ground you need.

2. You can't might be able to (see edit) connect to the ground for another branch circuit, but for a retrofit like this you may be able to run a ground wire to the ground rod or other grounding electrode, or the wire attached to the ground rod (grounding electrode conductor).

There is usually a grounding jumper in the dryer that you can install with a three wire cord. This provides protection in the event of a wiring fault without changing your wiring. Unless you're 100% sure you've got a good ground, it might be better to just set up the dryer for a three wire power connection.

edit: In locales where the 2014 NEC is adopted it is allowable to connect to the ground on another circuit provided the wiring goes back to the same enclosure, right size, etc. - that may or may not apply to the hot water heater or furnace equipment circuits.