What conditions do persons wishing to marry have to fulfill before a proper Hindu marriage can be solemnized?

Neither bride nor groom should already be married or have a living husband or wife. A divorced person, a widow or widower is free to remarry;
Both should have reached the minimum age for marriage: 18 years in case of the bride and 21 in case of the groom;

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Apart from being able to give their voluntary consent to the marriage, both must also be free of any mental disorder which could make them unfit for marriage;
The bride and groom should not be within the "prohibited degrees of relationship" nor should they be "Sapindus"1 of each other (these expressions are explained in detail in s.3 (f) and 3(g) of the Hindu Marriage Act). This rule does not apply if it can be established that a custom or usage is applicable to each permitting marriage between the two. Significantly, the rule does apply when the relationship is based on adoption.