You should definitely plan on getting a Worker very early on. In the past I've pretty much always waited until reaching size 2 and then immediately started my first Worker. But I find Lord Parkin and EscapedGoat's arguments for building the Worker right from the start pretty convincing.
There are a few potential reasons not to do the Worker first:
- If there's a sea resource within reach and you have Fishing then building a Work Boat first is kind of like having your cake (improved tile) and eating it too (city growth).
- If you lack appropriate technologies for your Worker to do something right away then obviously there's no need for one just yet.
- You want to concentrate on commerce first, presumably because you're chasing a religion.
- You could avoid building a Worker entirely if you can manage to capture one from a neighbor and get it back to your capital quickly. This isn't a move you can count on pulling off on a random map but it might make sense if you're confident that you have neighbors close by.
- It might be better to build a Settler first if you have reason to fear that land will fill up quickly. With anything like a normal map or normal number of opponents I don't think this should be a concern, however.
The long and short of it, though, is that your very first Worker is probably the most useful investment you'll make all game, and if you don't build one (or capture one, I guess) first thing then it should probably be the second or third thing you build.
The best time to build your first Settler is a lot harder to nail down. A lot depends on the map type, the lay of the land, the number of opponents, where they are relative to you, and various other settings. On a small enough map or one with enough opponents you might conceivably never build a Settler, and just conquer enemy cities instead.
With that said, if you're playing a fairly typical game--one where there's space for everyone to build several cities and you aren't feeling super aggressive--then I'd say a Settler should be no later than your fourth thing built. You'll almost certainly want to build a Worker first, and you'll probably want a Warrior or a Scout before you build a Settler as well. The first because of the many benefits already explained, the second because you need units to explore and find a place to build the second city, as well as protect the Settler from animals once it is ready.
It might make sense to delay the Settler until your fourth build if you included a Work Boat in your early builds, or if you lost a military unit in an early battle. The overall goal, however, is to get a second city, on a good location, as quickly as possible. The payoff from a second city, in terms of additional commerce, more resources, and the fact that you can now build
two different things at once is simply enormous.