I will ask students to help pass out calculators, reference sheets, answer documents, and manilla folders (for privacy). I will pass out the test document. I like to spend a minute taking a quick look over the various test sections. I do not read questions here, but I want to make sure that problems are not skipped and that all instructions are clear to everyone. I will then remind the students that if they finish early, they should review their test. This includes making sure their answer document has been filled in correctly, looking for silly mistakes, making sure their handwriting is legible, etc.
I generally like to pick up all the assessments at one time. It's just my personal preference. It seems to help me make sure I have everyone's test.