1999 oldsmobile silhouette passanger side wiper flew off the van

under the heads on the block

Remove cover at pivot point and tighten nut.

The gears in the wiper motor are slipping, Get a new wiper motor.

There is no adjustment on this you likely have a worn wiper arm transmission and the extra play causes the arm to travel to far.

when the wipers are off make sure the driver and passenger wipers are at same level on windshield
you can adjust them so they don't go off the edge or hit the bottom.
if they are hitting off the edge and hitting the bottom as well you need to check the linkage since it may be worn out.

You can learn how to replace the battery on the link below.

http://www.ehow.com/how_6112071_replace-battery-oldsmobile-silhouette-minivan.html

Good luck

How many miles on the transmission, and have you ever changed the trans fluid?

loosten drivers side wiper arm and bring up about an inch twards the top of the window. retighten and test.

are all the doors shut, if so could be a bad sensor on one of the doors.

Yes you can adjust them yourself. First you need to check that the wiper arms are not bent. If not, remove the cap at the wiper arm base, under it u will find a nut, remove this nut. you should now be able to remove the wiper arm. (it is comon for caravan wiper arms to be corroded on. If the arm dosen't come off, you may need to heat up the wiper arm with a propane torch. be careful not to melt the plastic cowel under the arm. OR you can use a wiper puller or a battery puller. do not force it, you can break the arm, DO NOT PRY AGAINST THE COWEL OR WINDSHIELD.
Once both arms are off, turn your van on and turn the wipers on. watch the wiper posts, turn the wipers off and watch the wiper posts return and stop in the "parked" position. Turn the van off. Install the passanger wiper arm first, it is positioned closest to the bottom an inch or two above the black cowel. It should be parrallel to the cowel. next install the drivers side wiper arm. it is positioned about 4 inches above the passanger wiper. again running parrallel to the cowel and passanger wiper. tighten the lock nuts down (do not over tighten) wet down your windshield with glass cleaner or windshield washer fluid and test wipers. If they still hit you can lower the passanger one a little or raise the drivers one a little (careful you don't raise the drivers one too much or it will 'jump' off the windshield at the top of the wipe).
good luck, hope this helps.