So you would be applying from the following link
https://www.visa4uk.fco.gov.uk/home/welcome, you'll need to register.
You can get your MiL to apply herself or you can apply for her...
The options under Reason for visit are:
Visit
Study
Work
Settlement
Transit
Other
Exempt
Then, VisaType:
Tourism
Child
Family
Business
Business (Academic)
Business (Creative)
Business (Religion)
Business (Sport)
Diplomatic / Official Visitor
Marriage / Civil Partnership
Private Medical Treatment
Permitted Paid Engagements
Other
Then if you choose Tourism, Visa Sub Type:
Visit - Tourism - 6 months
Visit - Tourism - Long Term, valid up to 2 years
Visit - Tourism - Long Term, valid up to 5 years
Visit - Tourism - Long Term, valid up to 10 years
Or if you choose Family, Visa Sub Type:
Visit - Family - 6 months
Visit - Family - Long Term, valid up to 2 years
Visit - Family - Long Term, valid up to 5 years
Visit - Family - Long Term, valid up to 10 years
So I think for your MiL, you have 2 choices on the standard visit visa:
Visit / Tourism / 6 months or Visit / Family / 6 months, most likely the later but whats the reason for the visit, is what you'll need to ask yourself.