There are several ways to maximize the space in your carry-on suitcase. It's a matter of deciding what works best for you. There are several keys that will help; however, and I list them below
1. If you travel a lot you would be wise to invest in good travel clothes that do not wrinkle. These can be found through several sources that specialize in travel products. Just do a Google search online for key words: "Travel clothing" + "wrinkle free." Any key words of that nature should take you where you want to go.
2. Utilize all the nooks and crannies of your carry-on luggage. There are often times indentations down the middle of your bag designed to allow for the handle, for instance, or some other feature. This is a great place to slip in such objects as sandals or flip-flops, a first aid kit or a toiletry bag. It fills the space so when you pack your clothing you are working on a level playing field, so to speak.
3. A lot of people sing the praises of rolling their clothes, rather than folding. The benefits of this are two-fold: 1) Rolling usually minimizes wrinkles, and 2) rolled items take up less space. Normally, you would roll such things as T-Shirts, camisoles and other knits, or even bras (if you are female), and underwear.
A rolled layer creates a cushioned surface for your next items, which would include skirts and pants, cotton blouses (if you are taking any, in which case you haven't listened to a word I've said here! Just teasing. Only you know what you will be needing, and most hotels do provide an iron in the room.)
Most carry-ons have a divider, so once you have filled the main space, you can shut the divider over it and go to work on the other side. You don't want your luggage bursting at the seams (assuming it has seams. If you travel a lot you may have already invested in a good fiberglas suitcase or something of a super strong material like polycarbonate), so most of your packing should already be done on the other side.
You can use this side for your underwear and socks or items you want to lay flat. Have you remembered your bathing suit or trunks? How about any dresses, or perhaps a sweater? Items you aren't willing to travel without, such as an adapter, recharging cords for your iPhone or iPad, your Kindle.
If you do this right, you can actually pack enough in a small 22-inch carry-on suitcase to accommodate you for a week! It's an acquired skill, but it can be done.
As I said, this is just one method of several that work effectively. Another proven method is the "bundle method," which is worth exploring also. Whatever method you use, the point is to pack what you need for the trip while not having to carry an abundance of heavy suitcases through the airports. It makes your trip a lot less stressful and buys you time in the long-run.