In informal spoken Welsh (i.e. normal Welsh), you can just forget about "nid" and use "dim" (which mutates to "ddim" when it comes immediately after the subject -- any word will undergo soft mutation in this position) to negate. "Nid" is used in literary and very formal written Welsh instead of "dim": "Nid ydw i'n hoffi" rather than "Dw i ddim yn hoffi". The only time you're likely to hear it in spoken Welsh nowadays is to negate a word other than a verb, which has been moved to the start of the sentence for emphasis: "Nid coffi dw i'n hoffi, ond te" = "It's not coffee that I like, but tea", but it still sounds very formal, so you can just use "dim" here too, as most people generally do: "Dim coffi dw i'n hoffi, ond te".
"Nad" isn't a simple negative particle, it means "that not", and is used in two cases: 1. when followed by the verb "bod" = "to be": "Ydych chi'n siwr nad ydych chi'n hoffi coffi?" = "Are you sure that you don't like coffee?" (with other verbs "na" is used instead); and 2. when followed by a word other than a verb, which has been moved to the start of the sentence for emphasis ("Ydych chi'n siwr nad coffi ydych chi'n hoffi?" = "Are you sure that it's not coffee that you like?"). But "nad" can also be replaced with "dim" (changing the construction slightly): "Ydych chi'n siwr bod chi ddim yn hoffi coffi?", "Ydych chi'n siwr mai dim coffi ydych chi'n hoffi?". You might not have learnt about "that" clauses yet, so you might prefer to just ignore "nad" until later on in your studies.