It's hard. Very, very hard.
First, you have to sit in a car for most of two days. You get a few breaks to stretch and run around, but you're mainly restrained in a car seat, watching the world pass by as you stare out the back window of the car. The ride can be tolerated as long as Mom and Dad stop early enough to give you time to relax and unwind before settling down for bed in a hotel.
Second, you have to be okay with eating, sleeping, and bathing in unfamiliar places. It can become overwhelming when nothing but Mom and Dad's presence feels ordinary. Even with Mom and Dad there, sometimes a meltdown is the only way to express and relieve the stress you feel.
Third, you'll arrive at your new home to find it's empty. Then, one day, a truck shows up and strange people pile numerous boxes into every space of the house. There's hardly room to move around, let alone play or find toys. You'll vaguely remember that these are the same boxes that were carted away from your old home. While you were once so interested in unpacking them, you now want nothing to do with them. You only want the attention of Mom and Dad because, again, it's the only thing that feels ordinary.
Lastly, prepare to get sick. The stress and anxiety from moving will take it's toll, resulting in an immune system that doesn't quite do its job as well as you would like. When you know your environment, being sick isn't fun. When you don't know your environment, being sick is beyond exhausting, resulting in extra crankiness, clinginess, and more sorrowful moods.
Is there any advice I can give to other parents out there moving with a toddler?
Be patient. Be calm. Be attentive. And be prepared to take much, much longer than you want to unpack your things.