Along with the normal movement there are a few hints to assist you in surviving so you will not lose health so often.
1. Try to look around quickly when your climbing and leaping over buildings so you won't risk a major loss of health from falling, it's easier if you have the parachute. Also, when chasing a target that is on the rooftops try to make sure you are away from any haystacks below so you don't end up doing a leap of faith and lose the target.
2. When in battle with multiple guards of diffrent types usually simply attacking will work, however if you are being attacked from behind try to counter it by holding R1 then pressing the attack button to counter. When facing targets that can't be countered like the Brutes usually kicking then ongoing attacks shall do the trick.
3. Handlings archers or gunners are easy, but at times they can really bother you during chase missions, it is best to have a crossbow ready so you can kill them faster.
4. On the panel with the four things you may use such as the hidden blade and weapons, it is handy to have the medicine ready and even better to increase how much can be held by buying poaches.
5. After the completion of the game you will be stuck as Ezio inside the animus, and can't exit the animus so it would be helpful to do missions that are outside of the animus before the end.
6. When taking down Borgia Towers it is best to have your recruits ready with "Arrow Storm" so that the Borgia Captain can be killed faster.
7. When running or sprinting on the ground it is best to avoid bumping into citizen, because they will make Ezio trip or fall over which will slow you down in missions.
8. Always try to reach full synchronization when doing missions, because they will unlock special missions that can help you understand Ezio's life better.
9. In multi-player try hard not to get spotted, and at the same time always be ready for anything, I suggest hiding in haystacks or small areas so you may blend well, try to notice how the person hunting you will stop many times to search for you giving you the idea to escape before they find you.
10. Always make sure your armor is fully repaired so you don't have less health then usual, repairing armor will be an issue if you unlock the "Armor of Brutus" after retrieving all six Keys of Romulus.