How can I confess if I did something wrong or against God in Hinduism? What confession methods are there in Hinduism?
Hinduism doesn't dictate confession because the core principle of Hinduism is "The jeevathma and paramathama are one and the same (advaitha philosophy)". All the wrong deeds are always done in presence of conciousness. For example when we do a wrong thing and realize that it was a mistake, we realize that mistake was done in the absence of conciousness, we even realise that there was a kind of absence of conciousness (which means conciousness was always there realizing that it seemed like absent during wrong doing). The realization of the mistake done itself is Confession. The wrong do=er, The mistake realizer, The person who decides to confess, The confession-er, The forgiver, The one who regret and The Suffer-er are all one and the same.
P.S: All my answers come from the combined experiences and the teachings of Sri Gurudev Atmanand [http://swamiatmanand.com/publications.php].
Krishna says in the Gita (Chapter 18)
Take refuge in Him alone with all your soul, O Bharata. By His grace will you gain Supreme Peace and the Everlasting Abode.
Fix your heart on Me, give your love to Me, worship Me, bow down before Me; so shall you come to Me. This is My pledge to you, for you are dear to Me.
Abandon all dharmas and come to Me alone for shelter. I will deliver you from all sins; do not grieve.
If you take shelter in the Lord, it is the same as the Christian confession. As Ramakrishna Paramahamsa said, what good are austerities if one has no love of God? What need of austerities if one has love of God?
The law of karma is inescapable. One must bear the consequences of ones deeds, good or bad. If one happens to die before bearing the consequences, one must be born again to bear them.
One way of looking at reincarnation is that it is simply a device to plug the one loophole in the theory of karma - that of a person dying before bearing the consequences.
It also explains why people who have done nothing wrong are suffering, why some are born rich and others are born poor.
The reason why Abrahamic religions have no use for reincarnation is because one can do a penance to get ones sins forgiven. Confession itself does not wipe away the sins. The priest will prescribe a penance, like '5 hail marys'.
Even there, the only reason to get ones sins forgiven is to go to heaven. Sinners would go to hell permanently.
So it is either karma + reincarnation, or forgiving of sins.
The rituals of 'ganga snaana' or dip in the holy river, or even a pilgrimage to holy places, are not about cleansing the sins, but more about purification - a somewhat different concept.
How can I confess if I did something wrong?
If that wrong affected someone in someway, the confession has to be done to that affected person.
Additionally: You can ask him/her, to give you chance for expiation "Prayashchit ka mauka". If that affected soul satisfied with you expiation, nothing will affect your karma. Think of it like this way, The wrong someway had to balance. You can neither create paap aur punya nor destroy paap aur punya. You only can exchange it, by balancing them.
or against the god in Hinduism?
For example you ate beef unknowingly? If your soul (antar-atma) claims you haven't done it knowingly. Then there is no questioning. As @Shiv said "The realization of the mistake done itself is Confession." We do have shuddhi karan and vairious methods for purifying our souls. Ganga snann is also a way.
There are only two things matter, first, whether your deed had affected your soul or other. Hence, you do need to confess and purify accordingly.
I am posting below the methods for removing one's sins. One of the methods is to publish one's sins to the whole world.
Vyasa said, 'By penances, religious rites, and gifts, O Bharata, a man may wash off his sins if he does not commit them again. By subsisting upon only one meal a day, that procured by mendicancy, by doing all his acts himself (without relying on the aid of a servant)....by becoming a brahmacharin and always ready for exertion, by casting off all malice, by sleeping on bare ground, by publishing his offence to the world, by doing all this for full 12 years, a person can cleanse himself from the sin of having slain a Brahmana. .....By living upon the scantiest meal every day for a space of six years, a person may be cleansed of that sin . By observing a harder vow with regard to food one may be cleansed in three years . By living upon one meal a month, one may be cleansed in course of only a year. By observing again an absolute fast, one may be cleansed within a very short time.'
Mahabharata Santi Parva, Section 36
REF: Ganguli's translation of Mahabharata, Santi Parva, Section 36
 Ganguli remarks in a foot note that the rule laid down is that he should eat in the morning for the first three days, in the evening for the second three days, eat nothing but what is got without soliciting for the next three days and fast altogether for the three days that follow.
 The harder rule referred to is eating in the morning for seven days; in the evening for the next seven days; eating what is got without soliciting for the next seven days; and fasting altogether for the next seven days.