Think of "had a nice day" as a name for an experience. You either HAVE an experience or you do not HAVE an experience. Yes or no! And, that answer may be different at different times. For example, I ate breakfast this morning so "had breakfast" is a name for an experience that I now HAVE so I can now say "I HAVE had breakfast". Your example speaks of an experience. To say you have that experience ("had a nice day") right now, you say "I HAVE had a nice day". To say that yesterday you HAD that experience you say "yesterday I HAD had a nice day". To say that tomorrow that will be an experience that you will have had you say "tomorrow I WILL HAVE had a nice day". The secret to understanding this is to treat "had a nice day" as the name of something. Do not think of the "had" within "had a nice day" as part of the verb of the sentence. Technically, it may be (and most people think it is but I disagree), but it is easier to understand if you don't think of it that way. Think of "I will have had a nice day" in exactly the same way as you think of "I will have had ice cream". Its thinking really is exactly the same. You do not really need to learn about the "perfect" tenses at all. You can ignore them. It would be better if nobody ever spoke of them. You only need to understand the meanings of "I had", "I have", and "I will have".

You mean the tense? It is the tense that goes before the past tense. Can you guess?

Past perfect

"had had" is the past perfect of "have." I know that it seems confusing, but it does appear and is perfectly normal according to the rules. The past perfect is always "had" plus the past participle (third form). In this case, the verb's past participle is "had" and thus we get "had had." The first "had" is simply marking tense, the second is the verb.