Historically, it has probably been exceptional for a laymen to use incense at home, because of the expense involved, and so it should not be thought that this is essential, but it certainly is permissible.
A laymen would only use a hand censer – not a swinging censer like the clergy typically use.
When a person censes with a hand censer, the censer is held in the right hand, and the sign of the cross is made with the censer over whatever he is censing. Then the censer is placed in the left hand, and he makes the sign of the cross and bows… unless he is censing other people, in which case he makes the sign of the cross with the censer only, and then bows to the people without signing himself.
If you are doing morning or evening prayers, you could cense before the beginning of the prayer, though some do this at the end.
It is a nice touch to have a Cross and Gospel in your icon corner. This is where your censing would begin and end. You could just cense the icons in the icon corner, but if you wanted to, you could cense the whole room you are praying in, or other rooms too, if you wish.