The Cell Stage is a fun and fairly short game that resembles a high end version of a number of feeding frenzy games. You just have to swim and not be killed. If you are killed, you won't lose much either. Just have fun and get used to the creatures in the game world.
If you intend to survive in the mania of the cell stage, then you need to be quick on your feet. Be ready to duck and weave between other organisms. If you are being chased by a bigger carnivore, then give them a herbivore to attack instead. You could also drag them into the attack range of any of the even bigger creatures around.
As soon as you can, put a spike on your backside. This makes it impossible for carnivores to attack you from behind. They'll just ram into your spike and hurt themselves. Electricity also works well for this purpose.
If you are a carnivore, you should also remember to put spikes by your mouth. This will drastically improve your attacking power.
If you are having trouble getting enough food, then you might want to put mouths on your sides. This will let you snatch food while you are moving through the level. This should really speed up your growth.
This goes without saying, but keep an eye out for any big explosions. This usually signifies a bit of meteorite being broken up. Swing over to the glowing spot to see if there's collectible DNA.
It doesn't matter whether you are a carnivore or an herbivore. Go ahead and get an omnivore mouth. Then keep it for the rest of the game. This will make food gathering much easier in the Creature and Tribal stages. You can only get the omnivore mouth in the cell stage though. After the cell stage, you will only find mouths that upgrade your current mouths.
You might not want to sell all of your cell stage equipment at the end of the stage. A number of parts, like the electric pods and flagella, are unique to this stage. If you sell them, you won't get them back later. Hanging onto them will allow for a few pretty cool options in your later creature designs.