Clothes in ancient Greece are basically just a variety of rectangles. The most basic garment is a chiton and that is essentially piece of cloth folded around the body in a U shape. The opening fell on one side of the body, under the arm. The garment is then pinned on the shoulder and tied at the waist. If you're really fancy, it might be sewn up on the open side or at the shoulders. Sometimes (especially for women), the garment would be wide enough to make sleeves by sewing/pinning at points along the arm.

The basic cloak is the himation, again just a giant rectangle of cloth (though usually a wool rather than linen) which men usually wore something like a toga, while women would often drape over their heads.

Now to get on to some of these other questions: for labor or sport a man would either wear a shorter chiton or gird the extra material up into his belt, female huntresses (more myth than reality, though likely there were women who had to do physical labor) also dress like this. Hunters might also wear animal pelts tied around their shoulders or at their belts.

Soldiers wear a distinct short cloak pinned on one shoulder called a chlamys (yes, like chlamydia), a traveler might also wear this as well as a wide-brimmed felt hat called a petasos and might carry a walking stick. Tall, knobby walking sticks appear to be a general affectation of aristocratic city boys as well.

A woman, particularly a higher class one, might wear a peplos, which is essentially the same thing as a chiton, just the top is folded over, creating a kind of ruffle that fell to the waist.

Clothes were expensive, so the wealthy had more clothes, more layers, thicker cloths, and more ornament. There's a little uncertainty over use of dyes and the ones they had were likely not very strong, but art suggests that the wealthy probably wore clothes with woven patterns on the edges. The poor would own less clothes and less ornate and shorter. Young children were probably only dressed as much as the weather demanded. Slaves also probably owned little or no clothing depending on what their work required.

If you're looking for some visuals, I would recommend taking a look at some images on ancient pottery (a lot of museums have pictures of their collection online), some of these tend to the less realistic end of the scale (eg, foreigners wearing animals skin and (!) pants, theatrical costumes idealized naked youths), but they can give you a good idea without the interference of modern aesthetics.