Learn Dutch: De rolstoel is voor de gehandicapte. - The wheelchair is for the disabled person.

This is a nominalized adjective—an adjective used as a noun. To turn the adjective gehandicapt into a noun referring to a person, you add an -e and use the article de. Together, de gehandicapte means "the disabled person."

Does de gehandicapte mean one person or a group of disabled people?

In Dutch, de gehandicapte is strictly singular and means one disabled person. To talk about multiple disabled people, you must add an -n to the end. "The disabled people" would be de gehandicapten.

Could I say het gehandicapte instead?

Not when talking about a person! When you turn an adjective into a noun to describe a person, it always becomes a de-word. You only use het for abstract concepts or things, like het goede (the good thing) or het onbekende (the unknown).

Why does the base word gehandicapt start with ge- and end in -t?

It is actually a past participle functioning as an adjective, coming from the verb handicappen (to handicap or disable). Because the stem ends in a voiceless consonant (p), the past participle gets a -t at the end. In this sentence, that adjective is then being used as a noun.