Note: due to the length of the texts, I won't copy it in here.
In Genesis 1, beasts were created before man.
In Genesis 2, man was created before beasts.
Genesis 1 gives the order of creation chronologically. The wording in Genesis 2 may seem odd, but this is what is suggested by the original Hebrew:
In 2:18, God says He will 'make' a help meet for Adam. The word used for 'make' is the Hebrew 'asah', which means 'to appoint'. If He was speaking of creating a help meet for Adam, the word would have been 'banah' (the word used when it says God 'made' Eve).
2:19 says, "And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.". According to the original Hebrew, this could very well mean that God had previously created the beasts and fowl, and was now bringing them to Adam. A lot of critics point out the word 'and' at the beginning of this passage, which suggests a specific order of events. But no word for 'and' appears in the original Hebrew passage. I will concede that the English translation does seem to suggest a contradiction of Genesis 1, but what the author of Genesis 1 wrote did not contradict Genesis 2.