how to find a job?

I am currently taking the CNA and PCT class at once. I really need a job with insurance and nights/and/or weekends. We can't put our kids in daycare because my son has a chronic illness and allergies and is too young to speak enough for care givers to watch him. I will be done with my class in August. how and when do i start looking for employment? should I write a cover letter since this is a career change for me and since i have desired hours?

thanks
Jess