First of all, these are pretty much options in name only: unless the company goes bankrupt (in which case, "options" and "shares" would be equally worthless), the price per share is going to more than $0.00001.
The vesting period is how long until you can actually use the options. You have a 36-month vesting period, so every month, you'll earn slightly less than 3k options. The cliff means that the options you earn during that period won't vest until right after the cliff point. In this case, after the three months, 8333 options (three months' worth) will vest.
The $1 isn't the worth of the options, it's how much you have to pay to use them. It's clearly just a nominal amount to make this technically an option rather than shares.
Normally, the value of an option depends on more than just the share price, but in this case the strike price is so low that you can treat them as being the same. If your company is publicly traded, then you can just look at the stock price. But "start up" implies that it's not. So the best approximation would be looking at how much money has been put in it. Look at funding rounds, if information about them is available: how much was raised, and for what percentage of equity? Dividing the former by the latter gives the market capitalization. If you know (or can estimate) what equity other people have gotten, you can treat that as funding (they are "buying" the shares with their labor).
Note, however, that venture capitalists are fund start-ups based largely on what they think their future value, discounted by their beta, is. Beta is a measure of risk, but is how much risk an investment adds to a diversified portfolio, and is lower than the investment by itself has. So if the value of this equity makes up a large portion of your holding, this means you're not well-diversified, and thus you should discount by a rate higher than beta.