Here's some basics on "Hammer follows slide" problems........
First, give the gun a thorough cleaning and fresh lubricant. Often used guns are full of fouling and dried lube and that causes all sorts of problems.
Most everything else is going to require disassembly of the frame, and unless you feel competent to get it apart AND back together properly and without damaging anything I'd take it to a good gunsmith or check to see if Colt will service it.
Possible causes of this could be a sear spring that's lost tension or has been altered by a previous owner trying to improve the trigger. This may need only re-tensioning the spring, or replacing it.
The hammer and/or sear may be worn or, much more likely they've been altered by a previous owner "improving" the trigger pull and ruining it.
Again, about all that can be done in this case is replacement of the parts. It's sometimes possible the sear can be repaired but usually it's ruined.
Here's a schematic of the .380 Government Model and some parts availability..........
Get the Colt 380 parts that you need to complete your project from Numrich Gun Parts. Order today!