Windjammer, sorry to hear about your pending situation.
All state UI laws are slightly different so it is difficult to know exactly what your particular state law provides. Generally you are entitled to claim 26 weeks of benefits during a 52 week period. This is often extended to 39 and in rare cases, 52 weeks, if your state's unemployment rate is unusually high. In general, you must report your earnings on your weekly claim. Under most state laws, any earnings over a nominal amount are subtracted from your weekly check. If you earn more than the weekly amount plus this nominal amount, you simply don't get a check for that week, but it doesn't count against the 26 week entitlement either. You still have the rest of the 52 week year to claim the remainder of the weeks of entitlement. In most states, there is a requirement that you seek work each week. In some you have to record the contacts on your claim. In others, you simply have to certify that you were available for work each day and looked for work that week. In all states I am familiar with, you do not get paid for the first week of umemployment, ie, you claim that week but receive no check. In most states you will be paid for that week after you claim a certain number of weeks (number of weeks varies by state).
As far as reporting your earnings on your weekly claim, if you are paid by a company which is covered by your UI law, that employer must report your earnings by SSN and pay unemployment tax on the earnings. That can and generally will be run against the claim SSN's at some point and the state will expect your reported earnings to match what that employer reported. If it does not, a potential fraud claim against you is possible.
My advice is to file your claim, in person or by internet, the first week you are unemployed. The sooner you file, the sooner you are eligible for payment. All UI agencies are connected in some fashion with a job search agency which has job listings and much support help with resumes, job search skills, etc. However, your best chance of finding employment is still yourself. The vast majority of people who find new jobs quickly, find them through networking with friends, acquaintances and family.
Above all, take heart. Your biggest challenge will be to maintain a positive outlook and keep trying. Remember, you are not umemployed through your own fault. It's just what happens sometimes. Good Luck and God Bless.