Despite being no longer a fan of formal skill systems, I'm still in favor of individualizing characters in ways unrelated to their class and vital statistics, ways that capture a bit of who they are rather than merely defining what they can do. This is a very basic framework only, because that's all I really need to get the effect I want. It's assumed that the chosen adventuring class is a character's primary focus, and that any other skills and interests are only peripheral dabbling.
Background is what the character did before he or she decided to run off in pursuit of adventure, fame, and fortune. In non-modern settings, almost everybody works from childhood on, and a player character is no different. Pre-teen and teenage years would have been spent learning the basics of some trade. Often this would be a family occupation, but a character might also have been apprenticed to another tradesman and learned a different craft.
A player should either choose or roll randomly to determine in what trade the character was brought up before being derailed into adventure. In most games, adventurers start young, and it's unlikely they've progressed beyond an apprentice level of competency. They're not going to master those crafts until and unless they settle down and leave the adventuring life behind. Their character classes are their careers now.
Nonetheless, they have picked up the fundamentals, and sometimes those can be of use in specific situations during an adventure. Rather than a detailed system to adjudicate specific abilities and results, the use of background skills in the game is best played out as a conversation between the player and DM. If a player thinks the character's background has some special relevance to the situation at hand, she suggests it to the DM, who makes a ruling.
"Deck hands do a lot of climbing in the ship's rigging. Crossing a rope bridge is somewhat similar, right?"
"I'm a farmer's daughter. Shouldn't I know something about how to calm a spooked animal?"
"I was apprenticed to a pawnbroker. Can I estimate what that painting would fetch on the market?"
The results should be fairly limited in scope: an automatic success on a minor action directly related to the background, a +1 bonus to a more important action or when the background is only indirectly relevant, a bit of information gained. The character should be able to assess the quality of items that pertain to his old trade with a fair degree of confidence, and to perform basic tasks. The rudimentary skills of a PC are not equivalent to the specialists listed for hire in the Expert Rules and elsewhere, and PCs should not be able to serve (competently, at least) as their own specialists, though they could easily act as assistants to a specialist if time and circumstances permit.
The real point isn't to give the players extra abilities, but to get them thinking in terms of what a character of a certain background would do and give them a point of identity to role play from if they so desire.
Below, a list of possible character backgrounds, choose or roll d30:
(1d3-1 for tens, 1d10 for ones if you don't have a d30)
1 Animal handler (Driver, ostler, groom, kennel keeper, beekeeper, etc.)
4 Artisan (Painter, sculptor, potter, glassblower, or other artistic profession)
6 Church, lay member
7 Craftsman (Carpenter, blacksmith, candle maker, wheelwright, cooper, tailor, tanner, cobbler, weaver, dyer, etc.)
8 Dock worker
9 Entertainer (Musician, singer, dancer, actor, juggler, fortuneteller)
12 Food preparation (Butcher, baker, brewer, chef, cheese maker, etc.)
16 Hospitality (Innkeeper, bartender, cook)
18 Law and justice (Constable, judge, lawyer)
19 Merchant, shopkeeper/peddler
20 Merchant, traveling
26 Scribe or cartographer
Obviously this list isn't exhaustive, and doesn't even attempt to represent the actual proportions of those occupations in a medieval or Renaissance society. It's simply intended to churn out some interesting results for player character backgrounds.