Ich mag das

This is the most common way you learn to say you like something. It literally means 'I like that.' Mag is the first person singular conjugation of mögen (to like).

A word about möchte. This is subjunctive of mögen. Ich möchten das = I would like that. You don't use this express you like something. You use it to express you want something.

Gefallen mir

This means that something please you. Die Schuhe gefallen mir means the 'The shoes please me.'

Notice that gefallen is the plural conjugation in order to agree with Die Schuhe (the shoes).

The sentence uses mir (dative) because person pleased by the shoes (me) is the indirect object. The shoes are pleasing to me - indirect object.

Schmeckt mir

This is only used when you are talking about liking food. It means that some food tastes good to you. Das Brot schmeckt mir. The bread tastes good to me.

Again the sentence uses mir because the person it tastes good to is indirect object that requires the dative mir.

Finden...Gut

This means to find something good. Wir finden das Haus gut. We find the house good = We like the house.

The literal translation would sound awkward in English in many cases. However, in German, this sentence sounds more natural.

Haben...Gerne

You use it to express liking something. Gerne is one of the cases where you can't easily understand how the use is word with grammatical English equivalents.

Technically, gerne is an adverb that modifies the verb it is next to, adding the sense of liking. Er hört gern Musik. He likes to listen to music. Here, gern is 'modifying' the verb hört, adding the sense of liking. So 'verb gerne' = liking the activity of the verb.

You also use the ich habe...gerne construction when talking about people rather things. Ich habe Sie gerne. I like her. There really isn't a good way to understand this with English grammar. It is just the German way of saying this.

Conclusion

So you have discovered a few different ways to say you like stuff. You don't have spend your German speaking life just saying 'Ich mag...' And you got a bit of a grammar lesson as well. I hope you magst this article.

Auf Wiedersehen!