The most important way to be safe on a dive is to plan what you will be doing before you go down. It is much harder to communicate below the surface. I have written a list of things you should think about before diving.
The Day/Night Before
Make sure you have all your gear
Charge your dive computer, if you have a watch.
Pack snacks for between dives
Pack a change of clothes
Have and pack Dramamine, if you will going on a boat dive
Make sure you rented or have a list of everything you will be renting
Prep defog (1 part baby soap, 10 part water)
For women, pack period products, and hair ties
Have your certification card and dive log
Charge your camera
The Day Of
Eat a light but filling meal
Water! and electrolytes
Get to the site early enough to sign in, prep your gear, and plan the dive.
Take more Dramamine, if going on a boat dive
Before the Dive
Who is your dive buddy?
Go over hand signals
Where are you going? What is the objective of the dive?
At what point will you turn around? Half a tank, etc?
Which of you is going to lead/navigate?
What is your emergency plan?
Have you checked out each other's gear to know how it works? Inflate/deflate, weight pockets or belt, purge pulls, etc
Is there a line, current, chain, and other water conditions you need to know about?
Do you have enough weight?
I'm sure there are more things to think about depending on the type of dive you will be doing, but this is a basic list for the average dive. Please comment with more tips if you have them! The best way to improve is to listen to others.
Enjoy your dive!