Avocados are dangerous to cut, due to their tough skin and slippery insides and pit. Slicing an avocado will depend on what you are using it for and how much of it you will be using. They also do not last very long at all once cut open. Even before they are cut, they go from hard to mushy fairly quickly.
I generally start with using the space that connects the avocado to the stem (there should be a little pill like thing; I shall be referring to this as the top), and cutting it in half. From there, I rotate it to separate the 2 sides from each other. When you start making slices, be careful how hard you press and you can hit the inside of the skin without piercing it and make slices without cutting your fingers. Slices are nice and can look pretty, but I prefer crosshatches. They are more manageable and easier to mash for spreading on wraps and sandwiches. Just squeeze from the top and bottom to the middle to push the avocado out if it isn’t coming out easily.
Removing the pit is kind of dangerous if you don’t know what you are doing. Knives slide right off, and if you are holding them the most logical way, your fingers are right in the path. I stab it slowly but firmly in the bottom of the pit (only a centimeter or so) and gently use the bottom of the skin as a lever like a seesaw to pull it out. Supposedly leaving the pit in helps prevent its aging, so only remove the pit when you are going to cut and consume it.