The Elizabethans had a broad variety of jobs which they could do. Many were still peasant farmers, the Wal-mart greeters of the Middle Ages. However, manufactured goods were made by craftsmen, not in factories, and each craft involved special skills and training. Metalworking was done by smiths, but not only by blacksmiths (who worked in iron, the most common and necessary metal), but also goldsmiths and silversmiths (who made jewellery) and sometimes even bronzesmiths.
Shakespeare's father was a leatherworker, but not just any leatherworker--he was a glover, which meant he made the soft leather used for gloves. These goods were expensive to make and if they broke, nobody threw them out--they were repaired. So there were people whose job it was to fix things, not only tinkers (who fixed pots and other metalware) but also such people as bellows-menders, like Flute in
A Midsummer Night's Dream.
Although many craftsmen would sell their own goods directly from the shop, they could also sell to merchants of various kinds. Some would wholesale to merchants in other cities, some would sell direct. Door-to-door salesmen were called chapmen (the "chap" part is related to our word "cheap")
Women could also make a living if they had to. There was a great demand for cloth of course, and that mean lots of thread. Unmarried women often made thread by spinning it then selling it. This was so common that "spinster" came to mean an unmarried woman. Women also were often involved in the brewing trade.
There were illegal activities as well, often combined with apparently legitimate fronts. The Chapman in The Winter's Tale is really a conman and thief, the spinsters in Henry IV Part II are prostitutes, and the tapster (bartender) Pompey in Measure for Measure is a pimp.
There were also other jobs we would recognize: doctors (Shakespeare's son in law was one), pharmacists (the Apothecary in
Romeo and Juliet), teachers (Holofernes in Love's Labours Lost), psychologists (Pinch in The Comedy of Errors), clergymen and lawyers (think of Hamlet talking to Horatio in Act 5 Scene 1: "Might this not be the skull of a lawyer?"). The army was also an option, and politics.
Oh, yes. You could also get into the entertainment industry. Shakespeare did.