Getting started with homeschool math in high school requires thinking about two things:
Where is my student now?
Where do we need to go? What are my student's goals?
The first question is easier. What math level has my student finished, when they were in school, and how well did they learn those concepts? Just because they have passed Algebra 1 and Geometry doesn't mean they necessarily mastered those concepts. Possibly they need to go back and brush up on Pre-Algebra topics. Or alternatively, perhaps they are talented in math and need to use a more challenging curriculum.
The answer to the second question: "What does my student need to complete?", depends on what their goals are, and how easy or difficult math is for them. Remember that you can decide what is an appropriate amount and type of math study to use. If your child needs basic life-skills math, then Pre-Algebra can cover that nicely. Or for some non-STEM community college classes they might need Algebra 1 and some Geometry basics. If your child is likely to pursue STEM fields in life or college, then you'll need to find resources to go up through Calculus.
Print-Based (textbooks, workbooks, worksheets)
Online/Video Based (either a live teacher or recorded lectures, with practice problems
Your choice of format depends on how your student learns best, and whether or not you will be able to help with math yourself or if you need to outsource that.
Math programs tend to be either:
Mastery-Based (learn the lessons, take the test, move on), or
Spiral (learn some new concepts, then circle back for frequent review)
This choice depends on how well your student retains information over time. Most students need "some" review, which you can work into a mastery-based curriculum just by going back occasionally to refresh previous topics. But if they need a large amount of review, it's easier to get a curriculum that has that built in.
Some ideas to consider as a starting place:
Print-Based: Used textbooks are inexpensive on Amazon, and the Holt math books are fairly user-friendly for learning at home. Remember that you can just do enough work so that your student understands the concept, not the whole page of problems! For students who need to back up and review, or go slower with math, try Learn Math Fast series of books. The name indicates the books are free of "fluff" that you find in traditional public school math books. Just the basics.
Online / Video Based: If your student learns best through audio/visual, try CTC math, which has self-paced recorded videos and practice problems on paper. Aleks online lessons walk you through automated lessons, for a subscription fee. For advanced / gifted students, try Thinkwell or Art of Problem Solving.
For more resources and ideas, see the Curriculum Pages.