Learn Italian: Io sono meno ricco di te. - I am less rich than you.

To say 'less [something] than', you use the pattern meno ... di. Here, you put the adjective ricco in the middle to make meno ricco di (less rich than). If you wanted to say 'more rich than', you would just swap it for più ricco di.

Why does this sentence use 'te' instead of 'tu' for 'you'?

After a preposition like di (than/of), Italian doesn't use the normal subject pronoun tu. Instead, it uses a stressed pronoun, which is te. That is why we say di te (than you) rather than di tu.

If a woman is saying this sentence, does she need to change any words?

Yes, the adjective ricco (rich) has to match the gender of the person speaking. If a woman is saying 'I am less rich', she must use the feminine form ricca and say Io sono meno ricca di te.

Can I drop the 'Io' and just say 'Sono meno ricco di te'?

Absolutely. Because the verb sono (I am) already tells the listener who the subject is, the Io isn't strictly necessary. Including it here just adds a little extra emphasis to contrast 'I' and 'you'.