It depends whether 'blame' is a verb or a noun. If it's a verb, you say 'blame someone' e.g. 'She blames me for the accident.' If it's a noun, you say 'put the blame on someone.' e.g. 'Don't put the blame on him for what happened.'

Blame someone :) Depending on what you want to say you can also say "blame someone ON someone/something": He blamed his lack of concentration on having slept badly that night. Does it help? :)

It depends on what you want to say. to blame someone: to say someone is responsible for something - He blamed the coach for the poor performance of the team. to blame something on someone: to say that something was the fault of someone - Don't blame it on me. Hope this helps.