The NIST (National institute of standards and technology) defines the HMAC standard as the following: $$\operatorname{MAC}(\text{text}) = \operatorname{HMAC}(K, \text{text}) = H((K_0 \oplus \text{opad} )|| H((K_0\oplus \text{ipad}) || \text{text}))$$ available in FIPS 198-1 (PDF).
I can see that the pre-shared key is XORed against internal padding and outer padding. I can also see that the results of which are not only hashed, but then concatenated together.
My question is how exactly is this used to ensure authentication/ integrity?
For example, If create a HMAC, how does my intended recipient use the HMAC sent with the message to ensure it is intact?
Also, given the inclusion of XORs, should I assume the inverse of these is calculated and somehow used in the process, as you can see I'm quite the novice, so some help would be very welcomed.