To + V v.s. To + Ving

My niece asked me a question yesterday:

In the following sentences, why does a V-ing follow the "to"? Shouldn't it be the root verb?

1. I'm accustomed to sleeping with the window open.

2. I look forward to going home next month.

Besides telling her the "to" here is a preposition instead of an infinitive "to," guess what else I told her so that she learned when to use V-root and when to use V-ing after "to."