Howdy, man. A couple little newb-to-newb tips in addition to the above.
1. If you don't already have a plan and aren't sure what else to do, I build a road first, before mine/water. Two reasons: it's the quickest worker action (so you get the resulting bonus for more turns) and the road helps other workers/settlers/military to move more quickly through the area and save turns of their own. There are plenty of cases (especially new towns) where you would want to water/mine first, but for me a road is the general rule if I'm not sure what is best.
2. Improve the tiles around your cities, but only tiles that will actually worked by the city. If a city is capped at size 6, don't improve more than 6 tiles around the town, since citizens won't be using the extra tiles. If start building an aqueduct later, THEN come back and improve more squares. On the other hand, DO make sure you improve enough tiles for all citizens to work. You're basically giving up free money/food/shields if a citizen is working raw land.
3. As an extension of #2, improve the strongest tiles first. Take a look at
this great page explaining terrain values, worker tasks, and managing your citizens. It gets pretty in-depth, I just picking up a few pointers from there has really kicked up my early game. You can use the ideas for any newly settled town.
4. Last, in addition to a worker improving tiles around each city, I like to have at least one extra worker (often more) focused only on building roads connecting all my cities. Even if you have to build roads through neutral territory, this is important. It allows you to quickly move military units to defend cities, resources/luxuries are shared among connected cities, and corruption is reduced in cities connected to the capital. This is one area that I think the AI considers a low priority, but I want that trade network connected ASAP.
Hope this is at least a little help. Good luck to you!