In level mode grow your plant to the goal plant size or exterminate all of the drones depending on the level. In endless mode grow your plant as big as possible. Change the game mode in the title screen's options.
If the ants kill the main plant then the plant dies, protect the plant by clicking on a stem and a menu will pop up to either spawn a sprout or evolve the stem. You can only evolve a stem into a root if it doesn't have a sprout on it. Roots will make the plant spawn more stems at their location towards the sun. Stems can't grow over other stems though. The green bar is the stem's health and the purple bar is the nutrients for the entire plant. Nutrients are used to spawn sprouts or to evolve the plant. When clicking on the plant or a root the blue bar is the water for the plant. If the water runs out the plant will start to take damage. Check the ingame manual's last page for some good ideas on basic strategies to grow with the plant.