"But and however are often used interchangeably to mean ‘yet’ or ‘nevertheless’... But and however have some distinct meanings of their own. •But means ‘on the contrary’ and ‘with the exception that’. I like everyone but her. •However can also be used to mean ‘by whatever means, condition or state’. I will get there however I can." Source: Onlinegrammar.com.au

The two words have the same meaning and function. 'But' is more common in everyday spoken language and in informal written language. 'But' is placed at the beginning of a clause and connects two halves of a sentence. 'However' is used in more formal spoken language and in neutral and formal written language. 'However' can be placed at the beginning of a sentence followed by a comma, at an appropriate position in the middle of a sentence between two commas, or preceded by a comma at the end of a sentence.

Chris' answer is quite thorough. Each word has several meanings and uses. I have a simple way of explaining the most common uses of both words. "but" means "the next thing I say or write in this sentence is very contrary/different/opposite of the first part of the sentence, for example: "I asked my friend to help me, but he didn't want to." "however" often means that the next part of the sentence will provide an explanation or additional information related to the first part of the sentence, for example: "I asked my friend to help me, however he couldn't because he had to study." OR "I would love to buy dinner for everyone in the world, however, I just don't have enough money." ......................... My explanations are very simple and are not really linguistically correct, however, they are simple:)

They mean pretty much the same thing. The only difference is that in formal, academic writing it is preferred to use 'however'.