Mögen is a verb you conjugate as
Ich mag I like
Du magst you like
Er, sie, es mag he, she likes
Wir mögen we like
Ihr mögt you (all) like
Sie/sie mögen you (polite form), they like
Here a page for more tenses, and other verbs

The forms of ein: I gave a pretty comprehensive explanation here a few days ago. If you want/need more, I'll be glad to oblige.

der, das, die works similarly, being respectively masculine, neuter, feminine nominative singular.
In singular accusative, they become den, das, die. Plural accusative is always die
In singular dative, they become dem, dem, der. Plural dative is always "den" (don't forget to add an -n ending to the noun)
In singular genitiv, they become des, des (masculine and neuter nouns take a -s ending), der. Plural genitive is always der

Hope to have helped, don't be affraid to ask, I'm often here. Viel Glück :)

Hi Liam,

Here is a link to a Youtube video where "mag" and "magst" are explained (by German with Jenny): https://www.youtube.com/watch?v=R4Ryj4X2W6g

Here is a link to a post where the usage of "die", "der", and "das" are explained: https://www.duolingo.com/comment/26832211

Here is a link to a post where "dein' and "deinem" etc. are eplained (unfortunately not "deine", sorry): https://www.duolingo.com/comment/26809786

Here is a link to a Youtube video where "einen" and "einem" are explained (by German with Jenny) (amongst other things, they are also explained in the video). https://www.youtube.com/watch?v=Ku4P3ac0puo

I hope that this is useful.