Boyd’s Bible Dictionary:

(pain). Capital punishment was by hanging (2 Sam. 21:6); stoning (Ex. 17:4; John 10:31); burning (Gen. 38:24); shooting (Ex. 19:13); the sword (1 Kings 2:25); drowning (Matt. 18:6); sawing (2 Sam. 12:31); crucifixion. The death penalty was inflicted for parental reviling, blasphemy, adultery, rape, idolatry, perjury. Secondary punishments were generally those of retaliation, an “eye for an eye,” etc. (Ex. 21:23-25; Deut. 19:18-21).

Concise Bible Dictionary:

The law required that capital punishment should be inflicted for reviling a parent, blasphemy, sabbath-breaking, witchcraft, adultery, man-stealing, idolatry, murder, etc. Capital punishment was by stoning (Deut. 13:10); burning (Lev. 20:14); the sword (Ex. 32:27); and hanging (Deut. 21:22-23). It appears that those who sinned at Baal-peor were first slain, and then hanged or impaled (Num. 25:4-5); the word is yaqa, and for hanging is used only here and in 2 Samuel 21:6,9,13, when the seven descendants of Saul were “hung up to the Lord,” which may also signify being impaled. There is no record in scripture of crucifixion being practiced among the Jews. Capital punishment was at times carried out in ways not mentioned in the law: sawing asunder and cutting with harrows and axes (2 Sam. 12:31; Heb. 11:37); precipitation (2 Chron. 25:12; Luke 4:29).
For minor offenses there was flogging, which was restricted to forty stripes (Deut. 25:3). A whip with three thongs accounts for the “forty stripes less one” (2 Cor. 11:24). Also placing in the stocks (Jer. 20:2-3). In other cases the punishment was according to the offense: “eye for eye, tooth for tooth” (Exod. 21:24-25). Imprisonment for definite periods was not customary as a punishment, though persons were imprisoned (Gen. 39:20; 2 Kings 25:27; Jer. 37:4, 18). Punishment was needed in the government of the nation of Israel, as it is in any nation now. God’s four direct punishments were “the sword, the famine, the noisome beast, and the pestilence” (Ezek. 14:21).
The Lord, referring to the law of an individual demanding an eye for an eye, enjoined forgiveness of personal wrongs; but this in no way interferes with civil government. Christians are exhorted to obey the ordained powers, pay tribute, etc.