In Spanish we use yo también/yo tampoco/a mí también/a mí tampoco for "me too" or "me neither" (so do I, neither do I) as a response to something that someone has just said where we agree with them.
Yo también = Me too/So do I
We use yo también when we agree with something another person just said. For example:
-Yo voy al cine todos los sábados. -Yo también.-I go to the cinema every Saturday. -Me too.
Yo prefiero comprar en tiendas independientes. -Yo también.-I prefer to buy in independent shops. -Me too.
-Miguel cree que aprender chino es muy difícil. -Yo también.-Miguel thinks that learning Chinese is very difficul. -Me too.
Yo tampoco = Me neither/Neither do I
We use yo tampoco when the person says something using a negative construction and we agree with their statement. For example:
-Yo no me acuesto tarde nunca. -Yo tampoco.-I never go to bed late. -Neither do I.
-Sara no tiene un salario muy alto. -Yo tampoco.-Sara doesn't have a very high salary. -Neither do I.
-Ellos no van a ir a la fiesta de Carlos. -Yo tampoco.-They are not going to go to Carlos' party. -Me neither.
A mí también = Me too/So do I (with verbs like gustar)
We use a mí también when the initial statement uses a verb with an indirect object or indirect object pronoun; if we agree we must also use the indirect object.
For example:
-A Claudia le gusta la comida libanesa. -A mí también.-Claudia likes Lebanese food. -Me too.
-A ella le encanta pasear por el campo. -A mí también.-She loves walking in the countryside. -Me too.
-A Miguel le molesta el ruido. -A mí también.-The noise is bothering Miguel. -Me too.
A mí tampoco = Me neither/ Neither do I (with verbs like gustar)
We use a mí tampoco when the initial statement has a negative construction and uses a verb with an indirect object or indirect object pronoun; if we agree we must also use the indirect object.
For example:
-A Javier no le interesa mucho ese libro -A mí tampoco.-Javier is not very interested in that book. -Neither am I.
-A mí no me gusta "Juego de Tronos". -A mí tampoco.-I don't like "Game of Thrones". - Neither do I.
Note that all these short answers can also be said to agree to something said in the past or in the future, (So did I, Neither will I,...)
For example:
-Ayer bebí demasiado. -Yo también.-I drank too much yesterday. -So did I.
-Irene no va a ir a la fiesta de Juan. -Yo tampoco.-Irene is not going to Juan's party. -Neither am I/will I.
In Spanish, when answering with yo también, yo tampoco, a mí también, a mí tampoco, we don't need to worry about the type of verb/structure used in the previous sentence. Unlike in English, in Spanish these short answers don't include any "do, did, will, have.."
-Miguel cree que aprender chino es muy difícil. -Yo también.-Miguel thinks that learning Chinese is very difficul. -Me too. -A ella le encanta pasear por el campo. -A mí también.-She loves walking in the countryside. -Me too. -A Claudia le gusta la comida libanesa. -A mí también.-Claudia likes Lebanese food. -Me too. Yo prefiero comprar en tiendas independientes. -Yo también.-I prefer to buy in independent shops. -Me too. -Irene no va a ir a la fiesta de Juan. -Yo tampoco.-Irene is not going to Juan's party. -Neither am I/will I. -Ellos no van a ir a la fiesta de Carlos. -Yo tampoco.-They are not going to go to Carlos' party. -Me neither. -Yo voy al cine todos los sábados. -Yo también.-I go to the cinema every Saturday. -Me too. -A mí no me gusta "Juego de Tronos". -A mí tampoco.-I don't like "Game of Thrones". - Neither do I. -Yo no me acuesto tarde nunca. -Yo tampoco.-I never go to bed late. -Neither do I. -A Javier no le interesa mucho ese libro -A mí tampoco.-Javier is not very interested in that book. -Neither am I. -Sara no tiene un salario muy alto. -Yo tampoco.-Sara doesn't have a very high salary. -Neither do I. -Ayer bebí demasiado. -Yo también.-I drank too much yesterday. -So did I. -A Miguel le molesta el ruido. -A mí también.-The noise is bothering Miguel. -Me too. 
