Bacteria and Archaea both prokaryotes. Remember that prokaryotes are single-celled organisms that do not have a distinct nucleus with a membrane or other specialized organelles.

Organisms in Bacteria and Archaea domains are classified based on their need for oxygen. 

• obligate anaerobes - die in the presence of oxygen
• obligate aerobes - die without oxygen
• facultative aerobes - can live with or without oxygen

Bacteria - are a very diverse group of organisms, they live in almost every environment imaginable! They are generally are found in three shapes

• rod-shaped (bacilli)
• spiral (spirochetes)
• spherical (cocci)

Read more about Bacteria, online at Microbiology Online, be sure to read the entire page, and take notes. 

Archaea are similar to bacteria in that they are prokaryotes, but they live in very extreme environments. You can read a short page on Archaea online at Microbiology Online. 

Then watch the Crash course video, Old & Odd: Archaea, Bacteria, & Protists