How do I convince an construction employer to hire me when I've been on disability for the last 3 years due to Cancer? My surgeries are over and they tell me I'm cured. However, how do I convince a new construction employer of this and how do I write it up on my resume?

The secret is to not include your illness in your resume. You want the potential employer to inquire to your work experience, not about your employment gap. The best thing to do is have a functional resume. Start your resume with a short couple of sentences on your qualifications, then show a bulleted list of areas of strengths and finally your professional experience with the organizations you worked for and their dates. This format will help show your skills in it's best light.
If you feel that you should explain your years away from the workplace, then you can include a short explanation in the cover letter. Also, while on an interview, you'll also want to focus mainly on your work experience, not on your illness. If the interviewer is concerned, they'll ask. Have a brief and positive answer ready, for example 'I was out of the business field for medical reasons but I am physically fit now and raring and ready to get to work!,' but don't feel the need to volunteer extra information.