It depends on your mouse and keyboard setup. Assuming you have the standard 2-button mouse and QWERTY keyboard though, you may have to use a hotbar change macro to sort through combos.
If you're using a gaming keyboard and mouse, a specific model may help people offering you a UI setup. I have a 6-button logitech mouse so my UI is going to be based on the fact I will always have 6 buttons available in my dominant hand, even while moving with WASD. I understand that's not going to be the case with you, so it's something to consider.
You can also use macros to play so you don't move your hands as much. Refer to this List of Hotbar commands as a source document for macros.
A very simple example of a hotbar change would be this:
Template: /hotbar change #
Example: /hotbar change 3
This immediately changes your primary hotbar (and all associated keybinds) to the abilities assigned to hotbar 3 (replace '3' with any hotbar you want to use: up to 10). You can change and switch individual abilities and slots as well, and that's in the manual above.
Using this macro, you can have one set that is your basic attack combo, one set that is a utility combo, and one set for mudras. It takes some practice, but should be pretty solid once you get used to it. Play around with it to configure the keybinds to your preference.
Don't forget to create a "/hotbar change 1" macro to change it back to your default hotbar.
Alternatively, there are players who simply create a complete rotation and order them in their hotbar so they just press 1, 2, 3, etc until the rotation is complete. This works very well for monks, dragoons, ninjas, and blackmages who don't deviate too much from a pre-determined rotation to optimize their dps. It's not so optimal for tanks and healers where flexibility is better than a good rotation.
If you want an actual graphic UI help: reddit provides inspiration.