Which is correct on this regard or in this regard?
The correct phrase is "in regard to." You may be confused because "as regards" is another way to introduce a topic. Many people believe both phrases are unnecessary business jargon. Better options, depending on the particular sentence, include "concerning," "regarding," "about," "in," and "with."
How do you use this regard?
With regard to is the only spelling of this phrase that you should use. It is the grammatically correct version of the phrase. With regards to is poor usage. An even better option, however, might be to use the regarding or another preposition like in or about.