Once she's been in the UK for 3 years and holds ILR, she's eligible. There are a few residency requirements, but unless she's been out of the UK for a significant amount of time, she'll probably be fine.
The first step is to apply - this can be done through her council (the Nationality Checking Service) or by post and costs £1005.
The first thing she hears about her application will be a letter asking her to provide her biomentrics. She'll take the letter to a post office and they'll take her photo and fingerprints.
She'll then hear if her application is approved.
Once it is, she'll book a Citizenship Ceremony through her council.
When she applies for her first UK passport, she'll be invited for a quick interview and once that is done, she'll receive her UK passport in the post.
After all the steps in the immigration process, naturalisation seems to be the easiest.
Here are the steps with links to the application form:
https://www.gov.uk/becoming-a-british-citizen/if-your-spouse-is-a-british-citizenEach application varies, but I applied in September, was approved after 2 months and scheduled my Citizenship Ceremony for a month later.
Here's the thread with current wait times:
http://talk.uk-yankee.com/index.php?topic=83234.msg1131260#msg1131260