Most printers have a combination of a pickup roller and a separation pad to pick the paper up one by one.
http://www.mgchemicals.com/products/408b.html
I used to use this on pickup rollers, cleans them and renews them a bit so they work well again for a while.
You can try using isopropyl alcohol on the roller to clean it as well.
The separation pad usually wears out and needs to be replaced, and it can be pretty easy to replace, just search your printer model and separation pad on eBay or around the web to see if you can find a replacement. Or sometimes cleaning it well to get rid of the smooth sheen will get it back in action for a while.
Otherwise yeah, considering brand new multifunction printers are $50 or less getting someone to fix it probably isn't worth it (unless it's an expensive printer to start with).