"Include" is the verb in the infinitive, so the translation is "incluir"
"Including" is the gerund, so it is "incluindo" and you use this form when the person is practicing the acting in the now.
Ex: "Ela está incluindo você o grupo"
"Inclui" is used in the third person singular, in the present. This form is hardly used. The gerund and the future is really more offen.
Ex: "Vou incluir você na lista" = informal and more used.
"Incluirei você na lista" = formal and hardly ever used.