Planning is key - which I see you're doing by posting this.

Around a day or two before your flight your departure gates will be confirmed (if you don't already have them).

Arrive at the airport around 3 hours before your flight departs to take into account any holdups e.g. security, walking to your gate, toilet/food breaks.

Also check the size and weight allowance of handheld luggage on the airline website to make sure you'll be okay. Most airlines allow you to take a free cargo luggage so it'd probably be worth taking one to be on the safe side too (so you don't have to find somewhere to wash your clothes on a constant basis.

Finally! Enjoy the flight! Like sex, the first time is always the best. (if you dont get motion sick that is) it's an amazing feeling during takeoff, like a rollercoaster but not as extreme. If you think you can hack it get a window seat, views can be amazing sometimes.

VLC wrote Planning is key - which I see you're doing by posting this.

Around a day or two before your flight your departure gates will be confirmed (if you don't already have them).

Arrive at the airport around 3 hours before your flight departs to take into account any holdups e.g. security, walking to your gate, toilet/food breaks.

Also check the size and weight allowance of handheld luggage on the airline website to make sure you'll be okay. Most airlines allow you to take a free cargo luggage so it'd probably be worth taking one to be on the safe side too (so you don't have to find somewhere to wash your clothes on a constant basis.

Finally! Enjoy the flight! Like sex, the first time is always the best. (if you dont get motion sick that is) it's an amazing feeling during takeoff, like a rollercoaster but not as extreme. If you think you can hack it get a window seat, views can be amazing sometimes.

Basically this. You just about covered everything. I would like to stress the preparation and arriving early. I have yet to run into any issues flying cross country like this, but I've also prepared every single time. Preparation is key, especially with travel.

What are you doing in California?
Make sure to give yourself a lot of time. Eat a good breakfast or lunch, but nothing too bad for you in case you get sick.
Don't be scared because nothing is going to go wrong.

Just like what everyone else said, but make sure you give yourself enough time for traffic, and security can be crazy sometimes. I usually arrive 1-2 hours early for flights at bigger airports

I fly a lot around the US, what airport are you flying out of? They generally tell you to get there 2 hours before your plane leaves, however if you're new it wouldn't hurt to come earlier. If you are going to a populated airport like LAX then plan on being there even 3 hours before your plane departs.

Airports are pretty easy despite all the chaos going around. You will follow the signs to departures and once you get in departures you will see signs showing what airlines are in that gate (fancy name for door). Sometimes in bigger airports you have 3 or 4 terminals (buildings) that hold different airlines so if you are in terminal 1 and your airline is in terminal 3 then just follow the signs for 3 then look for your airline once you get there.

Once you're at the door get your stuff out and go through the door. Some airlines will have a person at a desk that will help you and others just have a kiosk (some have both). I prefer the kiosk personally. Go up to the kiosk and put it what it asks for. Alaska will ask for your last name and flight destination and will give you your boarding pass like that, but ones like United will ask you for your reservation number. Make sure you have that number when you go in no matter who you fly with. If you have connecting flights make sure you wait at the kiosk because it will print all your boarding passes. From here take out your ID and hold your ID and boarding pass but put all metal things or anything in your pockets in your backpack and go to security. To find security just walk between the desks for the airlines and you will see the security line.

Security now is getting messed up. You have your general security line, you have your TSA precheck, some airports have Delta CLEAR (for delta members), some have United preferred (for United members), etc. I highly recommend getting TSA precheck if you can because you don't have to take off your shoes or belt, lines are usually smaller and you only go through a metal detector. Anyway go to your perspective line and wait. Once you are in the front of the line they will motion you to come up to them and you just hand them your ID and boarding pass. They scan the boarding pass, check the names, and give it back to you. Now throw that stuff in your backpack and you'll see a place where people are putting their luggage to get checked, put it on that conveyor belt (make sure it starts moving before you leave it), then right beside that is the metal detector or the scanner you go through. Once you go through then wait for your luggage. Sometimes they take it and ask you if they can look through it if they find a suspicious item.

Now you're through security so put all your stuff where you want it (shoes / belt on, phone in pocket, etc. etc.). All you need now is your boarding pass. See what gate you are and follow the signs for that gate (usually the signs are right above you as soon as you get through security). Get to your gate and keep your boarding pass and wait for them to call your group. On your pass it will show what group you are. Most airlines now only let boarding groups 1, 2, and 3 have a carry on and a "small personal item". The personal item is the backpack, purse, etc. Groups 4 and 5 only get the small carry on so make sure you either only have a backpack or you are groups 1, 2, or 3. Groups 1 and 2 are first class and priority boarding, groups 3 is for those who upgraded to economy plus / got priority boarding.

If you have a long flight I would highly suggest spending the money to get economy plus. That couple inches of leg room really does make the difference. You can get on the website and click change seat to see the seats available. If you get economy plus you will also automatically be boarding group 3. if you don't want to spend the money for the seat but want the carry on you can pay for the priority boarding which is usually $20. Economy plus can range from $30 up to $80ish. Keep an eye on the seats and check daily if you want to save money. My last flight (Orlando to Seattle) had a economy plus window seat going for $75 a month or so before the flight, but a couple days before the flight it went down to $40. My first class seat went from $551 to $350. First class is awesome but not worth the money. When you fly as much as I do sometimes its nice to upgrade yourself to it but economy plus is all that's needed. Southwest does not let you pick your seat, you just get boarding groups and pick your own seat on the plane.

Also your bigger airlines like United, Alaska, Virgin, Delta, American, Southwest, etc. offers free drinks and snacks so make sure you take them. Smaller ones like Spirit don't give free stuff and their seats suck lol. Airlines like Spirit are cheap but they are cheap for a reason. It's always worth the extra money to fly with a bigger airline.

Anyway I think that's about it. If you have any questions let me know!

EDIT:

There is no weight limit on carry on, just size limits (9 inches x 14 inches x 22 inches), if you're checking in a bag then the weight limit is 50 lbs.