Teaching your students to read and understand newspaper articles is a great place to start. This allows them to better understand the world around them, and it might make them more comfortable if it is a current issue that they already know something about. You could have each of your students do a report on one article in the newspaper, where they summarize what it was about and then discuss how it affects their lives. This is an easy way to make them comfortable reading the paper.
Another exercise is to have each class member read an opinion piece and then identify which parts of the article are opinion and which parts are fact. Then have the students write a response to the article. They can agree or oppose the statement, but should look for specific information to support their claim.
It is essential for adults to be able to communicate through letters and email. A good exercise is for the students to write a business letter. This could be a letter that disputes a false charge with their bank account, gives notice that they are moving or deals with any matter they might need to write a letter for. Be sure to teach your students how to address and format the letter correctly.
The students might also want to practice writing a cover letter for their application. This would work well with a simple class on writing a resume. It is important to teach the students what to include in a cover letter.
Many illiterate adults struggle with understanding the letters and notices that they receive from businesses and their health care providers. A few lessons should be spent on learning to understand what each of the letters is telling them. They should be able to find the corresponding phone number and come up with a list of questions to ask the person they would contact to clarify the situation. For medical information, they should be able to understand what they need to do and be able to ask questions about their condition or treatment.