The alarm system came with the house and we had a power outage. Now the system trouble light is on. How would I reset the alarm? Do I need to call a specialist? Or can I do it myself?

You should be able to reset but will probably have to enter your code.

Trouble may go away when battery comes back up.
What system do you have,is the Trouble light yellow? Try *2, it should show different numbers than zones. Those numbers tell problem: AC failure, Low battery, Failure to communicate, Low wireless device batteries, among other troubles.
Can you provide model# or picture of Key Pad, We work with DSC, Ademco, Napco, Caddx, Honeywell, ITI, GE, we service ALL.

Try to identify the touble code.

It could indicate a bad battery. They probably need to be replaced somewhere between 3 and 5 years. Quick power failures may sometimes mess up many kind of electronics.
Call the monitoring company. Remove AC power to the alarm. Unhook the backup battery. Wait about 1 minute. Replace with a new battery.

Before you go replacing Battery, be aware of Panel Tampers, If Monitored, Call them first, Or police may be dispatched. If you own system, changing battery never hurts.
Losing power and battery going low showing trouble is normal, and normally trouble goes away aftercorrect voltage is reached. The transformer may have been Knocked out.
Trouble code is important.