How do you recover after a coaster crash in Roller Coaster Tycoon?

Try switch to the red flag and click the red flag again, It worked for me in R.C.T.2 but I am sure it should work in the first version too.

An easy way to avoid a crash is to place brakes before the station platform. Also, it's best to have a mechanic that fixes only that ride. If your roller coaster crashes, double-click the stop light to reset it. This will reopen it, but more than likely no one will want to go on it because "It isn't safe." Best thing to do is to save frequently andd just load a file after it crashes.

Following up on Shek's answer, your coaster will suffer from reduced popularity because the guests will see it as unsafe. Frankly, the only way to get back up to your pre-crash numbers on it is to delete it and rebuild it. Fortunately, it's easy to save the coaster, delete it, and then build it from the save file. It will cost you money, since you're "selling" the original coaster, which has depreciated in value, but as a side benefit, you do get a new installation, which means the coaster will be more reliable.