My mother didn't pray her Wajib prayers for many years. As her son, and being the only child, do I have to perform her Qada prayers? If so, how should I get started given that I do not know how many prayers she had missed?
Bismihi ta'ala
Assuming that your mother has passed, besides whether it is wajib for you or not, it would be the most noble and most loyal thing for you to do. Your mother might have forgotten, or unintentionally neglected, or gone through some difficulties, and did not perform her acts of worship.
You, the loyal son, are able to compensate that and the reward and blessings will not only go to her, but to you as well. In some hadiths it says there are some children who are loyal to their parents while alive, and not loyal when they die. Being not loyal is not doing dua or prayers or good deeds for them.
If you cannot roughly estimate, or have no idea, you have two options:
1. Pray what you can, as long as you are healthy and have time. The bonus is it's extra 'ibadah for you, which is a wonderful thing.
2. You can hire someone to do the 'ibadaat on behalf of your mother. There are many poor mu'mineen/mu'minaat who live off doing 'ibaadaat hire. Pay for whatever you are financially capable of.
With prayers for your success.