Steam has, at this point in time, no parental controls available natively. You do, however, have a few options.
Windows 7 has a set of limited parental controls. The two relevant ones are time limit, and game ratings limiting. You can get to these by clicking Start > Control Panel > Parental Controls. These are per user, so if they are using your account to login, this won't work.
Time Limiting
This control lets you choose what hours in the day your child's account can use the computer. Any time outside these times, your child will not be able to use their account on that machine.
For you, this could be used to limit the hours in a day that your son/daughter could play, but it wouldn't allow for the 'X hours per week' type of control. It would also mean for things like homework or other related activities, they wouldn't be able to use the computer. You could of course bypass this with using a separate account and the second technique they support.
Game Rating Limiting
This allows you to control what type of games you want your child to be able to play. It supports multiple different Ratings Boards rating system (mine is ESRB, as I live in the US, though they support many more) and it allows you to control even down to what type of content should not be allowed (Blood, Nudity, Violence, etc). With this you can limit what types of games can be played.
Coupled with the previous method, this could be used if your son/daughter were to have two accounts. The first would be one where the could play video games, but could only do so for certain times of the day. The second cannot play video games (via this blocking method) and can be used to surf the internet, do homework, etc. It isn't the cleanest solution, but it is built right into the system you already have.
Alternatives
The alternative to the above is to get third party software. I have no experience with any of these pieces of software, but two that came up in a Microsoft help discussion on this topic are:
- NetNanny supports enforcing allowing only certain windows of time for software to run, and on an allowance system where they get so much time per X (day is all that is listed, but likely week and month are available as well)
- Cyber Patrol has the same support as above, where it allows time windows or an allowance per chunk of time.
As a F2P, you are restricted to a certain set of privliges, taken from here.
Q. How is a free account different than a premium account?
Premium accounts have a few extra features, including access to rare and
cosmetic items through random item drops, the ability to store more
items in your backpack, and more powerful trading and crafting
abilities. Otherwise, the gameplay experience will be identical for
both accounts.
What this is saying here is that, as F2P, you can only receive items, but you cannot send items out. As a premium player, you are able to receive AND send items to any player. There is one exception: items you receive in trades can be traded away. Item drops, however, aren't.
You need to buy something from the Mann Co. Store (or the Orange Box) to become Premium and gain the benefits of full trading.
For more information of trading, go here.
Best Answer
According to the official Team Fortress 2 Wiki page:
And to answer your question of "and if I hit this limit of gameplay, how do I tell?", I guess you could time yourself playing for 70 minutes, and if you don't receive any items, you've hit the cap.