The laws for those places that allow for common law marriages vary. In most cases there has to be evidence of co-habitation for a specific period of time, usually around 5 years. In addition, they couple has to have presented themselves as being ‘married.’ Such things as mail addressed to them as Mr. and Mrs., bills, invoices, even children’s school records can be used to show such things. Joint bank accounts are another indication.
First of all, you have to be in a jurisdiction that recognizes a common law marriage. If it doesn’t, no level of proof will be sufficient to prove it.