Typical beer recipe instructions are as you mentioned in comments
- 1 week primary
- 1 week secondary
- 2 weeks in a bottle
These instructions will work fine and make beer, but they won't necessarily make the best (or clearest) beer. Some suppliers have adjusted their recipes to the beer style, adding more time to the instructions.
In most cases, 1 week is not long enough for a beer to finish, but the secondary racking will kind of kick it along, though the use of secondary is questioned by some (myself included - I never secondary unless I have another reason to, like racking onto fruit or because I want a cleaner container), but the added time is helpful (whether you moved it or not).
Most beers finish fermentation within 7-10 days with temperature control, but this can vary widely depending on the yeast and temperature. However, even after fermentation is finished, most ales will benefit from at least some bulk aging at ale temps; improving the flavor. After that, cold crashing or lagering will help clear a beer (letting the ale sit at cooler temps - the cooler the better). Ales aren't wine, so we aren't talking months, although the stronger the ale, the more time it may take. Giving an extra week or two in the primary, and another week or two at fridge temps can have a significant positive impact on the flavor and clarity of an ale. Lagers benefit from much longer aging, especially at lager temperatures.
You can use fining agents, but time is also effective, though it may take longer. Most fining agents take a couple of weeks, which is a good aging period after fermentation is complete anyway, so you really can't go wrong with them. You'll probably find adding a 2 week period without a fining agent will also get you very clear beer, but that will depend on the recipe and method.
Aging will typically not benefit the clarity of a wheat beer, as the haze remains in suspension for longer periods (forever?). There is such a thing as kristallweizen, but that normally takes filtration.