There are three main points of non-biblical evidence for Jesus; Tacitus, Pliny the Younger, and Josephus.

Tacitus, in discussing Emperor Nero’s decision to blame Christians for the fire that destroyed Rome in 64 AD, (cited in Annals, 15.44):

Nero fastened the guilt . . . on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of . . . Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome. . .

Pliny the Younger also writes about Christ and the habits of Christians, in a letter dated AD 112 (Pliny, Letters, translated by William Melmoth, Cambridge: Harvard Univ. Press, 1935):

They were in the habit of meeting on a certain fixed day before it was light, when they sang in alternate verses a hymn to Christ, as to a god, and bound themselves by a solemn oath, not to any wicked deeds, but never to commit any fraud, theft or adultery, never to falsify their word, nor deny a trust when they should be called upon to deliver it up; after which it was their custom to separate, and then reassemble to partake of food–but food of an ordinary and innocent kind.

Josephus (in Jewish Antiquities, 18.63-64), mentions Jesus as well:

About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he . . . wrought surprising feats. . . . He was the Christ. When Pilate . . .condemned him to be crucified, those who had . . . come to love him did not give up their affection for him. On the third day he appeared . . . restored to life. . . . And the tribe of Christians . . . has . . . not disappeared.

Though it is not clear if all of this passage indeed came from Josephus, indeed some suggest that parts of it were altered, it seem clear that Josephus at least authored part of the above passage.

The Babylonian Talmud also mentions Jesus (probably authored somewhere between 70AD and 200AD, Babylonian Talmud, Vol. III, Sanhedrin 43a, 281). Here they use his real name, instead of the Greek “Jesus”, they use “Yeshua”, or in this case “Yeshu”:

On the eve of the Passover Yeshu was hanged. For forty days before the execution took place, a herald . . . cried, “He is going forth to be stoned because he has practiced sorcery and enticed Israel to apostasy.”

Lucian, a second centuray Greek Satirist, mentions Jesus in The Death of Peregrine, 11-13,

The Christians . . . worship a man to this day–the distinguished personage who introduced their novel rites, and was crucified on that account. . . . [It] was impressed on them by their original lawgiver that they are all brothers, from the moment that they are converted, and deny the gods of Greece, and worship the crucified sage, and live after his laws.

I will not go into detail on any of these accounts but instead point you to one source where there is more discussion, Ancient Evidence for Jesus from NonChristian Sources.