I've been to 2 "around the clock" showers. If you haven't sent out invitations yet, just choose some times of the day and night (for each guest) and enclose a slip in each invite that has that time written down. Guests are asked to choose a gift that relates to that time of day. People with morning times tend to give things like coffee makers and breakfast items, people with 5 PM may give wine glasses or cocktail shakers, people with late night times may give lingerie, but those are just a few ideas - there's plenty of room for flexibility and it's very loose! It's fun if you assign times in a random fashion, but if you want to cheat a little so the 80 year old grandmother doesn't get 1 AM and feel funny giving a teddy, that's fine too!
To open gifts, you can either do it randomly or go in order of the clock.
Every shower I've been at does the silly stuff like take all the bows and ribbons to make a fake bouquet to use at the rehearsal (use a paper plate and either tape things down or punch holes and thread the ribbons through). I've seen a hat created with trailing ribbons to be the "veil" during the rehearsal. That's more silly but the bouquet is actually useful so the bride actually has something to hold during the rehearsal march and to practice handing it off to the maid of honor.
I've also seen people write down what the bride says as she opens each gift - leave out what others say, and just put down her remarks. Then it gets turned into a fake "conversation" between her and her new husband on the wedding night.
Most showers of all types (bridal, baby) have someone recording the gifts and the donors so the bride has a list in case cards get separated from gifts, so having someone with a pad & paper doesn't look odd.
Have fun, whatever you decide!!