how much of my disability check will go to taxes

depending on your tax bracket, you would pay the feds.
You don't pay the State (at least in California).

I have been on SSD for four years now, and I have always had them withhold 10% for taxes. My wife works and we have always gotten a refund, except one year when we sold some stock and had to pay taxes on it. I think 10% is what the SSA recommends as a starting point.

After being on SSD for two years you will become eligible for Medicare Parts A, B, and D. Part A is free, but you have to pay for Part B and it will be deducted from your monthly check. If you elect to have Part D, you have to pay for that also.

If you mean your Social Security Disability Check it can be anything from 0%-100%. If you did not work then basically, none of your SS will be taxable. If you did work or had a lot of interest income then part of your SS benefit will be taxed. There is a worksheet in the 1040 instruction book to figure this out.

PS - I am disabled on SS but my wife makes her own money (much more than my social security) so about 75% of mine is taxed because we file jointly.

Best of luck, Mark