Regard (v.) is to consider or to have an opinion about something:
Picasso is regarded as one of the greatest artists in history.
I don't regard this as a problem; I regard it as an opportunity.
Regards (n.) is a greeting:
Please give my regards to your parents when you see them.
Some people end their letters/emails with the expression Regards, or With best regards,
The phrases regarding and in/with regard to mean "related to / concerning the following topic":
Have you read the report regarding the economic crisis?
Before finalizing the contract, there are a few points I'd like to clarify with regard to the deadlines.
These phrases are more formal, and in everyday spoken English we'd say "about" instead: "Have you read the report about the economic crisis?"
Regardless (adv.) means one thing is not affected by something else:
A champion keeps going, regardless of the difficulties.
The mayor approved the new law regardless of the opposition from the public.
I know we don't have all the information, but we still need to make a decision, regardless.
As you can see from the examples, the action (keep going / approving the law / making a decision) is not affected by the other situation (the difficulties / the opposition / not having all the information).
Don't use the word "irregardless" - it doesn't exist; it is a common error in English.