Initial Processing of the Grape Juice
What you get may or may not get immediately separated. Skin and seeds might immediately be removed from the juice. Separation may not immediately occur (especially for red wines), since skins and stems are an important source of "tannins" which affect wine's taste and maturity through aging. The skins also determine the color of the wine (see What is Wine).
Maceration (the time spent while skins and seeds are left with the juice) will go on for a few hours or a few weeks. Pressing will then occur. One way to press the grapes is to use a "bladder press," a large cylindrical container that contains bags that are inflated and deflated several times, each time gently squeezing the grapes until all the juice has run free, leaving behind the rest of the grapes. You can also separate solids from juice through the use of a centrifuge.
Aside: When I first started drinking Chardonnay, my tastes ran to wines with heavy flavors of oak (introduced in the barrel aging process by storing in wood barrels). Then I was lucky enough to be at the Acacia winery in Sonoma during harvest. The friendly people there had me take a wine glass and hold it under the device that was extracting juice from the grapes. Fending off the bees, which were very attracted to the sweet fluid, I got a taste of absolutely fresh unfermented Chardonnay grape juice. It was wonderful. I then knew what Chardonnay actually tasted like! From that point on my tastes have run to a different balance of oak and fruit flavors in the wine. The best way to learn about wine is to drink it. Sometimes it even helps if it isn't even wine yet . . . .