The basics?
Proper Protective Equipment or PPE is the first step. This should include eye protection, hearing protection, a helmet, chainsaw protective chaps or chainsaw protective pants and gloves.
Safe staring procedure is next. Never drop start a saw. That is never start a chainsaw by dropping it with your left hand holding the wrap around bar and your right hand on the pull chord. The safe methods are:
A log start-- With the chain brake on, holding the rear handle of the saw with the bar over a log and then pulling the chord with your left hand while pushing forward with your right.
Ground start-- The saw on the ground, your left hand holding the wrap around handle bar, your foot on the rear handle and pulling the chord with your right hand.
Crossed leg start-- The rear handle of the saw pinched between your crossed legs, your left hand firmly on the wrap around handle and your right hand pulling the pull chord. This one sounds weird but I find is the best way to start a hard starting saw as the angle of the pull is the best.
Next phase, sizing up the tree you are going to fall.
Where does the tree lean? The tree will not go fall against its lean with out some extra force being exerted on it. Establishing the lean is essential.
Looking for hazards where the tree is likely to fall.
Looking for hazards in the tree, dead or hanging branches, bees nests, etc.
Escape routes-- After you have determined the lean of the tree and decided on where you are going to fall the tree, you need to make certain you have a safe route of egress away from the falling tree. Most fatalities occur at the base of the tree and the simple act of walking away from the tree after it has begun to fall, increases your likelihood of survival. The safest route of egress is 45 degrees from opposite the direction you are falling the tree. Directly opposite the direction the tree falls is the second most dangerous place to be as the top could break out, hangers could fall, the tree could barber chair(rip the back strap off, smashing any body parts located behind the tree) or other trees hit by the falling tree can fall that way. Your escape route should be easy footing with no brush or stabs to trip you up. Spend the time and effort to cut a clear path. DO NOT cross behind the falling tree to access your escape route. Always finish cutting on the side of your escape route.
The pie cut-- The pie or relief cut, gives the tree a place to go and in combination with a back cut that does not connect to the front allows the tree to hinge in the direction you want it to fall . On a conifer with a gently lean, the tree can be felled 90 degrees to the left and 90 degrees to the right of the direction of the lean. If the tree is a heavy leaner then it should be felled in the direction of the lean. Your relief cut should be 1/4 to 1/3 the diameter of the tree. The angle should be greater than 30 degrees. There are lots of variables in how wide to make your face cut. Those will be considered in the intermediate class. Just keep in mind that when the face closes the tree will tear the holding wood and it should be committed in the direction you want by then. If you make a narrow face, it could break too early and fall in a less desirable direction or it could stop entirely(A very bad thing). If the face is too wide it could stay attached to the stump(Not necessarily a bad thing), mainly it just means a lot more cutting.
Now the face consists of two cuts a top cut and a bottom cut. To make it easy we will focus on standard cuts where the bottom cut is horizontal and the top cut is angled. I prefer to make the bottom cut first(there are whackos here who do it differently). On most professional saw there is a line on the side of the saw on the housing for the pull chord. That line is called a gunning sight. It is perpendicular to the chainsaw's bar and fairly accurately shows where the tree will fall if you have assessed the lean correctly. Prior to cutting pick an object as far away as possible as your target. As you cut 1/4 to 1/3 of the way in on your bottom cut make certain you finish your cut with the gunning sight facing the target. Now start you top cut. Keep in mind that it is better to miss short than long and that you should at least match up your cuts on your side of the tree. Placing a stick in the far side of your cut can help you determine if you top cut is long, short or dead on. If you are short you can take another cut at a steeper angle. If you are going long, either stop early or stop straight above your bottom cut and hit the pie section with a maul or falling axe. It should break out leaving a flat back. You can fall a tree with a flat back. What you cannot do is leave any kerf on the top or bottom(kerf is the line that your saw cuts). Any kerf or overlap will negate the effect of your face cut and become the default face cut. The tree when it falls will close the kerf first and do a variety of bad things like swinging away from the side that closes first, popping off the holding wood and going where ever it pleases, or just stopping(really bad as mentioned before). The back of your facecut must be a clean intersection of two planes resulting in a straight line perpendicular to the desired target.
Is this doing anything for you? Too basic? I could drone on more if you wish.