Hmm, that used to be something that we were taught early on when I was a child.
Basically the host is placed in a sacramental called a monstrance. It is usually made of gold which is a fitting setting for our Lord Jesus in the Eucharist. There is a little glass case in the middle in which the host is placed, surrounded by a wide surrounding of gold, often constructed in the appearance of rays. Sometimes the consecrated host placed in the middle is the larger on the priest uses at Mass.
With suitable ceremony, often a Benediction ceremony, the monstrance is placed on the altar and people come to pray for the duration of the Adoration. When I was a child we regularly had a 40 hour adoration. Now it is more often 12 hours or so. Yes, people really did come at night. I always like the wee hours of the morning myself since there are fewer distractions.
These used to be in the church in front of the tabernacle, now it is more often in the chapel where the consecrated hosts are reposed.
When entering the presence, it is typical if possible, to kneel on both knees and bow, rather than simply genuflect.
People sign up for a period of time to remain in adoration, typically for an hour or more. It is important to not leave Jesus unattended. People need to be in continual adoration. Others come in during that time also, it is just some take responsibility to see that the Presence is always attended.
People can pray in any way they choose, meditation, comtemplation, rosary, or just talking to our Lord and letting him know our love for Him.
For me, the atmosphere always seems dense (only way I can describe it) with the Presence and extremely peaceful.
Hope this helps to explain Adoration a bit more.