If there is nobody to make the answers, how does a priest celebrate Mass?
(1) The Extraordinary Form; the old Tridentine Rite either in its Latin form or said using the English Missal. Here the priest makes the replies - all of them - himself. After all, as well as being sacerdos he is also a member of the laos, the plebs sancta Dei. I find that even the Blessing at the end gives me no trouble; I think of myself as blessing the whole parish beyond the walls of the church. The Missal itself tells you how to modify the reply to the Orate Fratres; the only other change you have to make is that in the Preparation at the foot of the altar, like Michelle of the Resistance, you say the Confession only once and omit et vobis fratres/et vos fratres and then you say misereatur nostri ... nostris ...nos .... This information is given in reliable manuals bearing Nihil Obstat and Imprimatur, such as O'Connell. Remember that, although you are alone, you say every prayer with your lips moving and in a low murmur. This applies to both Uses of the Rite and is essential for validity.
(2) The Ordinary Form, aka the Novus Ordo. Para 211 of the General Instruction of 1969 said that the priest omits salutations and the final blessing, to which the Third Edition adds monitiones, advices. I take this to mean, for example, that the priest omits both the Orate Fratres and its response; that he omits the entire dialogue before the Preface; the Pax; Behold the Lamb of God; and so on. The Second Recension of the Third Edition completely revised the rites to be employed in this type of Mass; itself an indication that this form of liturgy is not obsolescent but a living part of the Western Rite. I give directions for how to do it simplified for when there is no server.
Having venerated and kissed the Altar, the priest stays at the Altar, where the Missal has been placed, and says the Introit; In the Name ...; Penitential Rite; Kyries (and Gloria); Collect. If possible, he goes to the legilium for the Ministry of the Word (and Creed); for the (optional) Intercession. Mass then continues as you would expect, with the omissions described in my last paragraph, until he has received Communion. Then he says the Communion Antiphon and does the ablutions either at the Altar (in which case the chalice is left at the side of the Altar) or at the Credence (when the Chalice is left there). Mass ends with the Postcommunion. He Kisses the Altar, venerates it, and retires.
This could be a rather brief Rite; I suspect most clergy will wish to use the First Roman Eucharistic Prayer so as to inject a slowing-down, and some gravitas, into the Mass. But why not take the oportunity to get chummy with the Old Mass?
Personally I find an early morning Private Mass a profoundly appropriate way to start the day. The main problem is that distractions creep in more than when I have a congregation ... but perhaps that's only my frailty. I do advertise these Masses, and sometimes they are not so private!