Advice for using professional movers (though some of this is relevant regardless) that I have learned from working at a moving company as my grad school gig:
If you have a lot of books, either get small boxes for them (alcohol boxes are good for this and you can sometimes get extras from your local liquor store) or put a couple layers in a bigger box and then fill with something lighter (my friend did a mix of books and puzzles last time she moved).
Related to the above point, try to pack boxes such that one person could lift them, but also don't have a bunch of boxes that have like one (tiny) item each.
Label! Boxes! With! Fragile! Items!
Also label boxes in general so we don't have to ask where every box goes.
Have a solid idea of how much stuff you have and if any of it might weigh over 200 pounds (that's where the heavy item fee kicks in at my company), because we Will Not Be Happy, or prepared for that matter, if you say 50 boxes and you actually have 100.
Put things that are not going in the moving truck off to the side.
For any furniture with drawers that open with gravity, either remove the drawers or strap them closed (or let us know during the walk-through that the drawers need to come out).
If you have furniture that might need to be disassembled, get a rough idea of how/whether it comes apart ahead of time. You do not have to do the disassembly yourself, but if we know up front we can time disassembly so it doesn't bring the process to a screeching halt.
Turn off and drain appliances that are going to be moved (AC units, fridges, etc.) in advance. I nearly dropped a chest freezer on my coworker because it leaked while I was carrying it and it got really slippery.
I don't know how other places work but my company charges hourly, so the estimate is just that--an estimate. You can cut down on how long we take by being prepared!
If the moving company is providing the truck, you will probably not be allowed in the truck for liability reasons. However if you get boxes to a spot that's more convenient for us to move things to the truck, that is very helpful!
When you are booking a company, give as much information as possible about elevator access and stairs (how many flights, if the steps are really steep, etc.). If there's an elevator we can bring flat dollies and carry stuff way more efficiently!
If possible, get any interior painting done such that everything is entirely dry on moving day (or just do it after).
Let us know about the parking situation! If parking is tight move your car(s) elsewhere to accommodate the truck if possible.
Send pets to a friend/pet sitter or shut them in a room that's been cleared in advance. If you have fish tank(s) or cage(s) move them out of the way of large items that need to be moved.
If you have kids, either get a babysitter for them or engage them in the process. I've encountered five year olds who were more polite and helpful than nine year olds simply because their parents set expectations and helped them to be involved.
Let us refill our water bottles in your sink. I've never met anyone who didn't allow this, but moving is incredibly sweaty and strenuous and if we stay hydrated we're less likely to drop that fragile item with sentimental value that you're really nervous about.
Tips! For a tiny job that takes ~an hour, $10-15/person is a normal amount, but if we're moving your entire house, tipping *at least* $30/person is generally a good move. However, I've only been truly annoyed by someone under-tipping when they clearly had money (the remote worker moving into a fancy apartment complex) and/or were rude (the guy who kept grabbing stuff out of my hands but not my male-presenting coworkers). We can accept food at my company; we cannot accept alcohol.
This is a lot of stuff to do! However! It will make things a lot less stressful for everyone involved, partially because you won't be doing all the logistical stuff the day of the move.
