what is the actual width of the joist?

Depends on how old your house is. Since about 1960 or so, 2x lumber is actually 1-1/2". From about 1920-1960, 2x was 1-3/4", and prior to that it was a full 2". Treated lumber is usually 1-5/8" thick.

As far as width goes, current sizes are as follows:

x4 = 3-1/2"

x6 = 5-1/2"

x8 = 7-1/4"

x10 = 9-1/4"

x12 = 11-1/4"

Treated will be wider slightly. Hope this helps.

Many older homes have hardwood installed directly on the joists beneath. I was in a older home where the home owners had ripped up the carpet, and exposed the hardwood beneath - I could see the basement through the cracks in the floor. Obviously the floorboards were installed perpendicular to the joists, and this illustrates where this rule came from. Todays homes have subfloors PL'd to the floor joists, with additional thin layers of subfloor or fibreboard laid on top of that to make rooms with different flooring types level with each other. You can't install vinyl or tile "perpendicular" to the joists, and neither should that rule apply to hardwood. The rule I stick to is "what looks the best"? Generally I prefer the floorboards to run from the main windows of the home. ie: front to back, so the eye is led through the house from the front door instead of across the house. If the house has a layout perpendicular to the front door, the floorboards would be laid down across the house, down the length of the hallways. The key is to support the floor with subfloor thick enough to support the wood floor boards - at least 5/8" and up to 3/4", making sure that joints in the plywood are supported by a joist.

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RE:

what is the actual width of the joist?

2 story home working downstairs i found the joist running in the ceiling. I know that the joist is a 2x6. but what is the real width of a 2x6 joist?

A nominal 2X6 measures 1 1/2" X 5 1/4". The largest dimension is usually refered to as the members depth.

1 1/2" X 5 1/2"

It's called nominal size. No lumber is the size it says it is.