1995 Pontiac Grand Am clutch problems

am having problems with my clutch the garage said there is nothing wrong with it but there is. I am very mechanical, I am by far no mechanic and know none of the names for any parts. Everything is a do-hicky. I was driving my 1995 Potiac Grand Am. I went to put it into gear and nothing. It would not go into gear at all. I had it towed to a garage. They found nothing wrong with it and acted as though I am just another stupid dame. I payed their $148 dollar for nothing I may add. It was fine for 2 days.Two days later the samething. I had one gear though, I think third. Ok I took it home took the air filter and hose off so I could see. Got my girlfriend to get in push the clutch and move the shifter. I could now see what was going on. There is this arm that reaches over and is suppose to hook to this other thing when the shifter is moved and put it into gear. It was just dangling there. I snapped it back into place and it was fine for a few more days. Again it did the same thing today. I snapped it back into place and it was fine. Well this is obviously going to be a re-occuring problem. Is this do-hicky hydrolic? Any suggestions, names for the parts etc......woodsy