The GIRM provides instruction for the use of incense during the celebration of the Mass as follows:
§ 277 The priest, having put incense into the thurible, blesses it with the sign of the Cross, without saying anything.
Before and after an incensation, a profound bow is made to the person or object that is incensed, except for the incensation of the altar and the offerings for the Sacrifice of the Mass.
Three swings of the thurible are used to incense: the Most Blessed Sacrament, a relic of the Holy Cross and images of the Lord exposed for public veneration, the offerings for the Sacrifice of the Mass, the altar cross, the Book of the Gospels, the paschal candle, the Priest, and the people.
Two swings of the thurible are used to incense relics and images of the Saints exposed for public veneration; this should be done, however, only at the beginning of the celebration, following the incensation of the altar.
The altar is incensed with single swings of the thurible in this way:
a) if the altar is freestanding with respect to the wall, the Priest incenses walking around it;
b) if the altar is not freestanding, the Priest incenses it while walking first to the right hand side, then to the left.
The cross, if situated on the altar or near it, is incensed by the Priest before he incenses the altar; otherwise, he incenses it when he passes in front of it.
The Priest incenses the offerings with three swings of the thurible or by making the Sign of the Cross over the offerings with the thurible before going on to incense the cross and the altar.
The General Instruction of the Roman Missal (GIRM) has this to say about the use of incense:
§ 75 The bread and wine are placed on the altar by the priest to the accompaniment of the prescribed formulas. The priest may incense the gifts placed upon the altar and then incense the cross and the altar itself, so as to signify the Church’s offering and prayer rising like incense in the sight of God. Next, the priest, because of his sacred ministry, and the people, by reason of their baptismal dignity, may be incensed by the deacon or another minister.
Seems to me like this was not a mass, so there are no restrictions for private prayer. Some people use incense in their private prayers, as do I when I pray on Solemnities. During lauds, on solemn occasions, incense can be used during the Gospel Canticle. I do believe that only priests should be able to incense the altar, as during the celebration of mass, not even a deacon can incense it. So I’m not too sure about the lay person incensing outside of mass.
During the mass it is acceptable for an altar server (a lay person) to incense the priest and people, in the absence of a deacon.