How do I know if it is a work from home job?
Make sure that it says either work from/at home or remote.
What should my internet speed be?
Now the simple way of know this would be to scroll all the way down to the bottom of the page and check the internet speed requirements. On another note: you should have the best possible internet that you can have. For instance: If you internet company has 3 different tiers (basic, fast and blast), you should get what you can afford but you want the best. Speed is everything when it comes to working from home.
What equipment do I need?
If you are going to be required to use your own equipment, you will be able to scroll all the way to the bottom and there you will see it. It is best to make sure that you keep your software up to date and try to have the latest pc (only a few years old). If they are going to provide a system to you, they will let you know.