“Would it be OK if I work from home today?”
You have a problem with your toilet. You want to stay home to wait for a plumber to come and fix it, but today is a work day. You need to ask your boss for permission to stay home, but still continue to work there. You call and ask this.
Would it be OK if I work from home today?
This is a good, friendly way to ask for permission to do something. You can use this phrase when asking for permission from a boss, a teacher, a parent, or anyone who has authority over you.
Hey, would it be OK if I take this Friday off? My son has a soccer game that I wanted to attend.
Use this phrase when you want to be polite, but you're also confident that the person you're asking will probably give you permission.
You also use this phrase with friends when you want to do something that will affect them. It sounds polite in this situation too. For example:
Would it be OK if I use your computer for a minute, just to check my e-mail?
"Working from home" is when you usually work in an office, but for a few days or a short period of time you do your work at home instead:
I'm working from home today, so call me on my cell if anything important comes up.
You can also use the phrase "work from home" to describe someone who always works at home, but works for a company that's somewhere else:
I love my job because they allow me to work from home.
You wouldn't use it, though, for a person who is self-employed. You would say "work at home".