Modern-day bottling tends to fall under one of two categories, and depends on the type of beverage that you are intending to bottle. The two types are distinguished by the method in which you seal the top of the bottle.
Crown Seals are generally used for bottling beer and similar beverages - generally carbonated drinks with a (comparatively) short shelf-life (measured in months rather than years/decades). Crown seals are a metal cap that is forcibly moulded over the lip of the bottle and is strong enough to hold in the pressure of the carbonated drink within.
Corks are generally used for wines of various types. The cork is longer-lasting and allows the wine to breathe a little - thus allowing the wine to mature. However, they do not stand up to the pressure of carbonation. If a "sparkling" wine is to be bottled - it must be put under a specialised cork assembly used for bottling champagne.
Cork bottling is supposedly very late period, as well as very early period. Apparently it was a "lost art" for many hundreds of years, and was only just being re-discovered at the end of the 17th century.