Thirty seconds after start up my car will only rev

My car is older than I am. It just recently started do this thing where she will drive for roughly thirty seconds immediately after start up. Soon after, whether I am in gear or not, she will only rev up. Example: I start her up, put her in drive, make it to end of driveway, then my speedometer drops to zero and my rpm's will increase when I step on the gas.
Theoretically, I could drive my car in thirty second intervals, and when she has her little "hiccup" turn her off, start her up, and drive for another thirty seconds, but I would much rather know what the actual problem is and know if it is something an up and coming mechanic with no actual ASE certification could accomplish.
Thank you for your time.