Step 1
Jump as high as you can. You will land in a different spot on earth each time you land (the earth would have rotated under you). Continue jumping until you land on the same spot that you started on. Take the number of times you jumped, multiplied by the distance the earth rotated under you during each jump. The answer will be the diameter of the earth (of course your would have to do your jumping at the equator for an accurate answer). My most current result indicates the earth is 24,900.89 miles in diameter.
Step 2
Take two stop watches and a comfortable chair. Setup your chair where you can watch a noticeable spot on a the horizon. When the sunrise is centered on the spot you have picked, start the stop watch #1. The next sunrise when the sun is centered again on your spot, stop stop watch #1 and start stopwatch #2. Do this for the next 365 days, each time writing down the time that had elapsed on the running stopwatch. Total the 365 times and divided by 365 for an average. My average was exactly 24 hours.
Step 3
Take 24,901 from Step #1 (rounded off for clarity purposes) divided by the 24 hour average from Step 2 and the answer is the earth rotates at 1,037.5 miles per hour.