Every single student I teach struggles with this topic. 

In Spanish, the verb "gustar" means "to please". Therefore, the order for the sentence won´t be something like "I like that", but "that pleases me". Therefore, the verb will agree with the thing or person who pleases. The pronouns are indirect object pronouns me, te, le, nos, os , les, and there are plenty of verbs using a similar pattern. 

For example, "you like me" is really "I please you", therefore is "te gusto"'- note the verb ending agrees with I, as it is me who pleases you!

To name a few: 

Darle a uno asco- to find disgusting (me da asco esa comida)

Hacerle a uno gracia- to find something funny (me hacen gracia esos niños)

Hacerle a uno falta- to need  (me hacen falta unos pantalones nuevos)

Darle a uno pena- to find something sad (me da pena que haya tanta pobreza en el mundo). 

Then, if you want to specify more you can start with "A + pronombre mi-ti-él-ella- nosotros-vosotros-ellos  nombre propio), which also allows you to combine different receivers of the action

Example: a mí y a mi hermano nos gusta la paella (note it is not *gustamos). 

It is a fascinating topic, and an essential one to master to achieve true fluency in Spanish. The other one is Subjunctive...worth another post!