You will need to create a situation where people are talking about the past actions of somebody and where there is doubt about what that person did.
You could describe a situation where a group of friends are talking about a party they went to the previous evening. Two of their friends didn't turn up and they're not sure what happened. ONe person is very reliable and was known to be ill yesterday; in this situation, you can say "he must have stayed at home". You can describe the other friend as being unreliable and students can provide sentences such as "he might have gone to another party"; "he might have gone to the cinema with his girlfriend"; "he might have stayed at home".
By using the same situation and two different people you can show how the speaker's opinion affects which verb form is used.
All the best,