To me it seems reasonable that someone who is unemployed would earn extra money by tutoring, mowing lawns or other odd various odd jobs. However are earnings like this allowed when you are also receiving unemployment benefits? I know this varies from state to state so let's just say the focus of this question is on California.
(In California) You can earn up to 25% of your benefit amount(gross pay) before there is any reduction in your unemployment benefits. Once you reach 25% of the pay there is a reduction in your unemployment benefits. However that 25% is not counted.
So (for easy math) if you have Unemployment benefits of $400 and you make $150 in odd jobs. 400x25% = 100 so you can make 100 before any reduction in benefit. So 150-100 = $50 in benefit reduction so total benefit amount for that week would be $350. If you only made 100 there would be no reduction in benefit.
With odd jobs and jobs that pay cash the only way that the government knows you made that money is if you tell them. Not telling them is Fraud and if you get caught the penalties can be painful.
Please note that the reductions vary by state. In Illinois you can make up to 50% of your benefit amount before any reduction but once you hit that 50% the entire amount of your earnings(including that 50%) is deducted from you benefit amount. This site has a list of all the states and their Unemployment sites where you can find specific information on your state.