I just got a new electric clothes dryer to replace a gas dryer. Unfortunately, I don't have an outlet that will fit the plug that came with the dryer. Can I just buy a adapter for it that can go from the dryer to a regular plug ?
Assuming this is in North America, No, you can't plug an electric dryer into a regular plug. An electric dryer requires 208-240 volts and possibly as much as 30 amps of current, and a standard plug supplies only 110-120 volts and 15-20 amps.
You will need an electrician (or knowledgeable acquaintance) to run high-current wiring and install the correct plug for your dryer.
Alternatively, you could return the dryer and replace it with a new gas dryer.