Older verb forms and pronouns from early modern English sound archaic to modern ears. Most of Shakespeare's work will sound archaic to modern English speakers and is a wonderful source of commonly used, archaic English. Early translations of the Bible into English are also a source of commonly used archaic grammatical expressions in English. The use of the subjunctive was also much stronger in early modern English and will sound strange in many instances. Some examples are below:
Using the now obsolete singular forms of you:
Thou
(to) thee (direct and indirect object form)
thy (possessive before a consonant) thy friends
thine (possessive before a vowel) thine estates
Outdated verb forms include
to do: I do, thou dost/doest, he/she/it doth/doeth, we do, you/ye do, they do (past: didst)
to be: I am, thou art, he/she/it is, we are, you/ye are, they are
thou shalt
Here's an example from Shakespeare's Romeo and Juliet. Note that certain words modern speakers anticipate to have a certain meaning actually have a completely different meaning (i.e. wherefore means why, not where).
O Romeo, Romeo! Wherefore art thou Romeo? (O Romeo, Romeo! Why are you Romeo?)
Deny thy father and refuse thy name. (Deny your father and refuse your name)
Or, if thou wilt not, be but sworn my love, (Or, if you won't, swear you love me)
And I'll no longer be a Capulet.