What a tremendous blessing! Certainly, you would be welcome to walk in at any time. HOWEVER…if you can sign up for a specific time slot (some parishes break them down by the hour, some by the half hour, some even by 15 minute increments) that’s better. The reason why is that when the Eucharist is exposed in the monstrance, it is NEVER to be left alone. So, those who are responsible for coordinating perpetual adoration must ensure that there is always someone present as a “guardian” of the Blessed Sacrament.
If you’re going to go anyway, it would be a big help to the coordinators to know when you’re there, as it checks a specific time off. But, then you need to make sure you actually come at your appointed time.
As for what you do when you go in, yes, you can genuflect the same as you would when entering any church. After that, it’s open ended. Some people pray the Liturgy of the Hours. Some pray the rosary. Some pray the Chaplet of the Divine Mercy. Some pray the Stations of the Cross. Some read Scripture. Some listen to Christian music. There’s really no wrong way to adore our Lord.
I hope this helps!