After buying seed bags from Tom Nook's, you can plant them to grow flowers. As an alternative, you can wait until every 6am and 3 to 6 flowers will spawn at random locations in town. Simultaneously, the same number of flowers will wilt as well. To prevent wilting, simply water a flower once. Raining or snowing will prevent wilting flowers too. Also, running over flowers will destroy them, so be careful about this.
Special Plants
Clovers and dandelions are special kinds of plants similar to flowers that grow in town from late February up to early December. Clovers are very sensitive, as they get destroyed once you try picking them up. Only the rare four-leaf clover doesn't die upon getting picked up and you can even wear it as an accessory. Dandelions eventually turn into dandelion puffs and the seeds gets blown away into the air.
Weeds
Everyday 3 weeds will appear in town. You have to dig them up yourself to remove them, so the more weeds around, the more laborious and exhausting clean-up will be. One of the biggest disadvantages of time travelling is the outbreak of weeds upon arriving at a much later time in the future. It could even take hours to manually remove all of the weeds that affected your town.
Worse than weeds is the incredibly annoying Rafflesia. It is an enormous ugly, red flower that cannot be picked up or dug up unless you pull out all of the weeds in one whole acre. This shows up once there are too many weeds in the town.