Usted, tú, ustedes, vosotros

In English, the pronoun "you" is used both in formal and informal contexts. In Spanish, there are four equivalents of English you... But it depends ... on the variant of Spanish , yes !

When you speak to a single friend , you use tú. The verb is then in second person singular - these forms mostly end in -s :
Tú vas a Madrid - You go to Madrid.
In Spanish, you can omit the pronoun, because the verb says clearly what you mean, so you can say simply : Vas a Madrid.

When the language is formal, more official, tú is not the best choice. You use "usted". What is important, after usted you use the third person of the verb :
Usted va a Madrid.
It's as if you said "your grace goES to Madrid".
And yes, it's possible to omit "usted" and say simply: Va a Madrid.
Of course, "Va a Madrid" can mean both : you go, he/she/it goes. The context decides what you mean.

And what if you denotes more persons than one ? In English there is no difference, though you can say "you all" if you want to stress that you is plural. Now the fun begins : it's different in Spain and in Latin America.

In Latin America , you use "ustedes" in all contexts. Ustedes is plural of usted and yes, you use the third person plural with it :
Ustedes van a Madrid.
It's possible to omit "ustedes" : Van a Madrid.

In Spain, in an informal context there is "vosotros". It's plural of "tú". Vosotros governs the 2nd person plural.
Many teachers don't teach this form on the basic level, because it's used only in Spain and you must use a special form of the verb:
Vosotros vais a Madrid - or - Vais a Madrid.
But it's important to know that this form exists. And in Argentina, it's slightly different :).

Spanish grammar Verb conjugation Most frequent Spanish words