How do I grow more orchids from my existing one?

Not really feasible in the home. Most Phals are mass produced using meristeming, a form of tissue culturing. And don't even think of growing from seed. I used to do it, made my garage into a lab, difficult and time consuming.
Many orchids can be divided to produce more plants. Sometimes a seperate plant with it's own roots will start growing from the main stem of a phal. We call them keikis, hawaiian for a small child. These can be cut away from the parent plant and potted up. Most people simply get the next phal that catches the eye, there are hundreds of clones out there now. Do yourself a favor and go to an orchid show, if there is one anywhere near you. You'll see way more than phals.

the first answer is correct, growing from seed is difficult. Phals do not make seed pods easily, most are so hybridized their pollinia is next to sterile. They sometimes make keikis that can be divided from the mother plant but it is not all that common. If you want more Phals then just buy more they are cheap and a dime a dozen.