It is best to be honest on the application since the employer will be doing a background check anyway and will find out about your past. If you don't put it down and you sign the application this would lead to problems.
There is a book out there that is specifically for ex offenders and I think that it would be extremely helpful to you. The name of the book is: 'The Ex-offenders Job Hunting Guide' by Ron and Caryl Krannich. You can purchase it at most book stores or may find a copy in your local library.
You may want to consider working with a Temp Agency or a Job Agency (ones in which the employer pays the fee) to assist you in finding a job. There are incentives for employers to hire ex offenders - they get special tax credits. You can also visit your local Job Service Center or CareerLink office (this is the old unemployment office) for assistance. They offer a wealth of information and free help to those seeking employment.
Hope that this is helpful to you. Good luck with your job search.
Whats your conviction?