This is roughly what I did to change my front sensor:

Unplug the battery
Jack the car up and remove the driver side tire (it's easier to see/access the plug with it off)
Unscrew the sensor from the pipe
Unplug the sensor (tricky part because it's pretty tight in there)
Screw the sensor in and then plug it in
Connect the battery back and the computer should have been reset

Should I still be getting a check engine light because I am. Is it possible that the rear is bad too? Or does the computer need time to adjust to the new sensor and then the light will go out?

Thanks

Leave the battery unplugged overnight. That'll forsure reset the computer.
If the CE light comes right away then possibly you put the wrong 02 sensor in. There are a few different 02 sensors depending on your model. (eg. with or with airpump. turbo. non turbo)

What code do you have?

I don't have a way to check codes. I was told by the dealer that my O2 sensor was bad. They reset the engine check light once and told me if it came back on within 5k miles it was shot--at this point I am not sure if it was the front one they were talking about now--after 5k miles, the light is back on.

go to autozone and ask them to reset your check engine light.