Synthesizing items is a big part of the Kingdom Hearts franchise, and this allows you to not only create amazing weapons, but also to create useful items like healing items that will serve your nicely while playing the game. The basis of the item synthesizing is to kill enemies and get loot from them, then use this loot to create the item you want.
Most enemies in the game drops some sort of synthesizing material, but some materials are much rarer than others. If you want to synthesize the best items for late-game playing, then you will need a lot of rare items that will take you quite a while to get your hands on.
Anyway, here's how to synthesize items in Kingdom Hearts 3. First off, head to a Moogle Shop and interact with this. These shops are found close to all save points in the game, so you will encounter them frequently. If that's not enough, look for a blue symbol on the map to locate them.
You should have an option to synthesize items in the Moogle Shop drop-down menu. This gives you a list of all the items you are able to synthesize, so just locate the recipe you want, see if you have all the ingredients, and click to synthesize the item! It's actually very easy to synthesize new items in Kingdom Hearts 3, as long as you have all the materials needed.
You can even synthesize upgrades for your Keyblades, which is a great way to spend any excess materials you come across.
And that's all there is to synthesizing items in Kingdom Hearts 3!