Repeating a lot of what has already been said;
A squashy bag is best to fit stuff in without breaking the rules. If you're going to be going regularly, it might be an idea to get a bag of the particular dimensions - e.g. Cabin Max do them in specific sizes for different airlines.
I have a clear plastic wash bag that I put all my liquids in. You can get travel sizes of toothpaste, and of spray deodorant. Decant your shampoo, conditioner, face wash, mouthwash, etc. into smaller bottles, and put them all in the wash bag. Put the wash bag at the top of your luggage so you can just take the whole thing out to go through security. All hotels will have some form of soap and towels.
Packing cubes are an option, but I usually find it's just as easy to roll clothes up small, rather than folding them. Just to state the obvious, if you're packing an extra pair of shoes, you can put rolled up underwear/socks inside them to save space.
Plan your wardrobe, and add an extra set of underwear, just in case, and possibly a small top/t-shirt in case you get sweaty in the afternoon and want to change before going out in the evening.
Don't forget a plug converter for your destination country if you're taking any electronics. You can often find USB sockets in hotel rooms, or even on the back of the TV in the hotel room for charging phones (don't forget your charger cable).