This page of the Final Fantasy 7 Remake guide has a detailed description of the HP and MP regeneration.
The basic way to regenerate HP and MP is to drink potions. You can buy them from traders, vending machines or find them during exploration.
Destroying crates scattered across the game world is a good idea. Some include items that restore HP and MP.
Some of the skills will allow you to regenerate health. You can, for example, develop Tifa so that she can strengthen your character. This build is described on the page dedicated to this heroine.
Beds and benches
In the game world, you can find beds and benches. The latter are more common on the streets. You can use them even during missions. In this way, you will fully regenerate HP and MP.