How to train for Cyclecross Races
Your training should really focus on three main components:


Fitness
Technique
Mental
Equipment


I ranked mental third, not that it should be considered near the end, but that getting the first two components in order should give you the confidence needed to tackle the third.

1) Fitness

As long as you can reasonably handle the bike, your fitness will be the most decisive factor.  There are three main fitness components:


Threshold power.  This is essentially how much power you can hold for an hour (the length of most CX races).
Sprint power.  This is used to sling shot yourself out of the corners and to grunt up short steep climbs.
Running.   For the times you are not on the bike.  You should try and get in at least one run every week leading up to the season.


2) Techniques


Mounts and dismounts. Practice these, lots! Depending on the series you may encounter many obstacles demanding a dismount. Proficiency here will be a big benefit.  


You can practice this on a grass field, walk beside the bike and practice dismounting then high stepping over the saddle and onto the pedal in one smooth motion. Your dismount should should leave your cranks level with the right pedal forward, when you re-mount you want to smoothly step over the saddle and onto the right pedal clipping in and pushing down in one smooth motion.  This takes practice. you may also need to improve hip flexibility.  The ideal should be that you step over and into the bike with your right leg. 


Once you can do the remounts smoothly at a walking pace, you can up the speed and start to practice the flying re-mounts. The technique is almost identical, except you land on the inside of your thigh and slide down your thigh onto the pedal.  You do not want to crash onto the saddle (if you value your reproductive organs).

In terms of dismounts almost everyone now uses a single dismount technique (there used to be a could different dismount techniques (e.g., stepping through on the dismount side) but these are inconsistent and high risk). The safest dismount is unclipping your right leg, bringing it over the tire and around to the outside of your left leg.  You will then unclip, landing on your  right foot.

Sliding the bike You will also need to get used to sliding the bike through slippery corners.  This can take some getting used to. Often unclipping the inside foot and being prepared to tripod can help, but unclipping slows down getting back on the power, so if you can avoid it then great!
Riding sand and mud if you have never ridden either on skinny tires (i.e., 700x33 not mountain bike tires) then you will need some practice. You will need to get your weight over the back wheel and let the bike float. You can only guide the bike in the general direction of where you want to go, its pretty hard to pick exact lines in the sand and mud. 
Riding off-camber corners these are tricky, especially on wet muddy grass. Its really about learning how far you can push things until the bike slides out. You need to experience it to know where the limit lies.
Sharp corners many courses can have a number of short, sharp turns. Practice these, with special attention to carrying as much speed as possible through the turn and accelerating hard out of the turn.
Picking lines this includes picking the smoothest line through rough terrain as well as how to setup and execute both sweeper and sharper corners  
Riding steeps many courses will have some short climbs that are almost wall like.  Practice riding these so you know ahead of time what it takes to climb these and whether or not you can climb. If not, you will need to dismount and shoulder the bike.
Shouldering the bike. There are about 3-4 ways to shoulder the bike which are optimal under different conditions and for different body types.  A youtube search should help there.
Carrying the bike.  Sometimes you only need to carry the bike a short distance (e.g., over barriers).  In this case shouldering is overkill. Here practice dismounting, then carrying the bike by the top tube. Make sure the saddle is to the outside of your arm, otherwise you will jam the saddle under your armpit limiting how high you can lift the bike when running over barriers.
Gear selection. Practice gearing down to an easier gear before a sharp corner so you can accelerate hard out of the corner. Similarly you need the correct gear before short sharp climbs.


3) Mental


A health reminder that this is actually all just for fun!
Realistic Goals
Visualizations prior to the event
Honest, non-judgemental assessments post race of your strengths and weakness.  This is a good life skill for many things. If you have a tendency for self-doubt or negative talk try not an let it enter here, its not particularly constructive and could be a bad habit worth kicking.


4) Equipment


How to set your air pressure. This is easily one of the most critical bike settings. The lower you go, the more traction you get, but the higher likelihood of getting a pinch flat or damaging the rim. If you are running tubeless you want to reduce the pressure until you start folding the tire over in corners, then adding just enough pressure to stop it from folding.
Tire selection - because CX is so traction limited choosing the right tire can pay huge dividends.
Keeping your bike in good running condition. Pretty self-explanatory.  If the wheels are rubbing the frame and it doesn't shift gears properly, it will be pretty hard to race.