Some plants (and shrubs) can be increased with soft cuttings.

Some can be increased from root cuttings.

Some need to be started from seeds only.

Things like ground covers can be rooted easily. I've done pachysandra and ivy this way.

This link is typical of some on the net:
http://www.ces.ncsu.edu/depts/hort/hil/hil-8702.html

Some plants that are fleshy... like sedums, coleus, impatiens can be started in a glass of water. Some houseplants can be done this way too.

Each plant has its own requirements. So you need to look it up and see what it needs. There is no "one rule for all" when it comes to plants. But increasing is affordable, and I've done it for years, including seeds.

You need a soil mix that is mostly sterile like a good seed starting formula or horticultural grade vermiculite. I typically mix 1/3 vermiculite to 2/3 seed starting mix when I do my seeds. This prevents fungal attack called damping off or rotting.
If you reuse containers, soak them in bleach water and rinse before using. Or use plastic yogurt cups after washing. These are very plentiful around HERE! Some carry out containers for food wash up well and are handy for making cuttings or sprouting seeds. Make sure you make holes in the bottoms so excess water can drain out.

Rooting powders are available in most nursery supply stores. They come in little foil envelopes for ease of use and affordability. (can be expensive and you only need a little pinch after all).