It's not a big deal. I would drain it out and replace all the oil (and filter if you ran it). It may smoke for a little but won't hurt anything. If it's a high mile car it may even clean it out a little bit! Good Luck!
Its going to tear up the engine
you will have to have it towed to a shop to have the trans flushed; do not drive it!!
You failed to mention what fluid you accidentally put in. In any case, have the transmission fluid flushed out and replaced with the proper ATF right away.
Have it cleaned out and flushed immediately
Your car will run (poorly) during that tank of gas and it will smoke like crazy while the transmission fluid goes through the engine. Secondarily, the transmission fluid (being very high in detergents and cleaners) will clean your injectors and top end of your cylinders quite nicely. Not a recommended way to clean them, but if you get it in there accidentally that will be the silver lining.
I am not a mechanic, but I know you have a problem. I would suggest draining the transmission and replacing it with the proper fluid. I wouldn't drive it because I think that might worsen the problem.
You need to get the trans fluid changed immediatley
Then you need to "accidentally" remove it ... pronto, which may mean flushing out the entire coolant system if the engine has been run.
to the transmission, not the engine
You should never add transmission fluid to a Chevrolet 350 engine. You can add transmission fluid to the transmission through the transmission dipstick holder.
The transmission will fail.
NO!!!! do not do this, oil is oil, transmission fluid is transmission fluid, and antifreeze is antifreeze, do not mix any of these, it can perminately damage your engine.