The qualifications required of a paralegal can vary dramatically throughout the legal industry, for three specific reasons. There are rarely any standards which delegate expressly what a paralegal can do or is supposed to do.
Often a paralegal who works for one firm may completely differ in responsibilities and duties from a paralegal in another (or even from another paralegal within the same office!) The third reason, is that because paralegals are often not licensed positions, there are no set standards of education required to gain a job as a paralegal.
Primary, what any organization hiring paralegals is going to look for is a basic understanding of administrative work, either in the form of training or experience.
Experience in typing, writing, filing, organization, and correspondence is primarily going to be a must for anyone working in an office capacity. Usually then, anything that indicates training has been received in administrative services or software application would be beneficial to a resume.
Also, displaying a background in a specific field that could be applied to law can make one desirable, especially to a firm that has expertise in that area. And thought it may seem obvious, a paralegal must display either an adequate knowledge of the law or an enthusiasm for it.
Fundamentally, at least some training in paralegal work, even if it is a concentrated multi-week course can be beneficial, but for someone who is looking for on the job training, it can be almost as important to have administrative credentials as well as background of knowledge that an employer can take advantage of, as well as a stable work ethic.
What any potential paralegal needs to show is fundamental capability which can overrule either a lack of experience or training.