Is a shop vac supposed to blow while vacuuming? We've had this for several years and I don't recall it blowing air OUT while I am vacuuming.

it is supposed to vent

connect the hose on the other end where it say vacuum not blow.

it is supposed to blow out the other hole. in order for a vacuum cleaner to suck things up, it also takes in air. That air passes thru a filter leaving the debris inside the canister, and then exits thru the other hole.

This video will show you.
http://youtu.be/-gCukdig57I

Cleaning filters on a bagless vacuum helps but filters should be replaced frequently, as often as every 3 to 6 months on some vacuums. Foam filters aren't as critical to replace because the pores are very large (which also means they don't filter out the small particles) so they don't clog as easily but paper filters have much tighter pores which become clogged and restrict the airflow. Cleaning paper style filters with water which can pack the fine dust into the pores clogging the airflow even more.
I recommend replacing filters st least onceor twice per year and cleaning them after each use for best performance and longer vacuum life. Blowing the dust out with an air compressor is my preferred method.
Changing filters frequently on a bagged vacuum isn't as critical because the bag collects most of the fine dust, dirt and gunk. The surface area of a bag is much greater than that of a filter so a bag is less likely to get clogged than a filter. Most homeowners change the bag once per month which keeps the air flowing smoothly.

On the shop vac there should be 2 places to insert the hose. One for blowing air and the other for suction.

remove the cap that directs the air and insert the hose in there.

fell on top of vacum for the place where the air is being sucked in that is the vacum port put hose on this port

should have a exhaust filter in the hole. it is round and 5-6 inches long with a type of filter on the end.

Has the cover got tabs that is suppose to catch when it's installed? check and see if there are broken plastic ends either on the vac or cover. It should be able to catch to hold it on.