I was in a hurry to finish the game before Procjam ends and I was unable to do a proper tutorial.
To help you started:
Collect as many small dots as possible you have 1000 in the start. Press enter and modify genome. Experiment with different options. There is also a help in the main menu. To level up your genome you must find grey circle things (however each one require different method of unlocking). When you modify genome keep in mind that plant is growing in four directions denoted by up, dw, lt, rt. It is possible to make it behave differently for each direction. Genome is executed from top to bottom. Most important are the roots which are like new plants. Enough of these and plant will grow huge fast.
Example for UP direction
If you put two dots for left two for forward and four for root it will have 50% chance that plant will turn left 50% that it will go forward in up direction and 48% chance that new root will be created. If a new root is created the process will be repeated for it.