Yong Huang writes:

Our carpet is 7 years old. It's quite dirty on the stairs especially
near the edge of each riser. I'd like to hear some good tips about how
to clean this part. I'm thinking of renting a steam vacuum cleaner
from Kroger or Home Depot. I don't think I should drag it on each step
of the stairs as I do on the floor. But using an attachment (if
there's one) won't have enough sucking, will it?

My friend's Hoover SteamVac DualV allows up to 140F or 60C degree
water. I didn't check Kroger's renting cleaner yet. But isn't 140F too
low for a good job? I know "steam" is a misnomer but I heard the
hotter the cleaner after the job, except perhaps the carpet won't be
very soft if the water is too hot. Correct?

Can you also recommend a few brands of detergent?

Sounds like you are over analyzing this.
If you have very dirty carpets, just about anything is okay.

I bought one of those Hoover wet vacs.
Works very well, just use the carpet cleaning solution that
comes with the unit.

Rental units work too.