How would you take care of a generic plant?

It depends on the plant, how I have to start, and the conditions around the plant.
Starting a seed is usually the same for all plants. Place the seed in soil about 1 inch down, and keep the soil damp and in sunlight until the seed sprouts. This can take anywhere from a day with commercial grass seeds to weeks with wild seeds. Some exotic seeds need to be exposed to heat or high humidity to grow. Others can only be started by planting sections of the plant itself, like violets or potatoes. Some plants are unable to reproduce, like seedless fruits, so they must be grafted onto a living plant instead.
Next, when the plan has grown a bit, I transplant the seedling into an environment more suitable for it's species. For example, in Texas I can leave my pet cactus outside unless it rains, but when I raise seeds gathered in Colorado, I have to keep them inside with a grow light so they stay cool and dry. Some plants need large containers, such as bushes and trees. Others are good with tiny pots or little planters. Some, like beans and peas, need trellises to climb.
As the plant grows further, you may need to keep growth in check. It is normal to prune rosebushes, or cut off sections that may be draining energy from the plant. Drooping branches over power lines should be cut. 
Eventually, you may want to replicate your plant. When this day comes, you can read about how to harvest the seeds, as it can be a lengthy process for some plants, or attempt a cutting from the plant. This can be achieved with root hormone and a sharp blade.