Can I use the output from a DRBG directly as K for AES, or do I need to use a key generator algorithm? NIST has 3 validated "Recommendation for Random Number Generation Using Deterministic Random Bit Generators" (DRBG's) that are based on NIST SP 800-90A:  


Hash_DRBG (based on hash functions)
HMAC_DRBG (Based on Hash-based message authentication code)
CTR_DRBG (based on block ciphers)


If I need a 256-bit key for AES encryption, by using one of the above mentioned DRBGs and getting output from it as K, can I use K for AES encryption directly? or I must use K as an input of other algorithm that is called key generator and the output of key generator will be key?
It you need a deterministically derived key for AES, the DRBG algorithms of NIST SP 800-90A are suitable, and their output is directly usable as an AES key. An example use case is when computing an AES session key from a longer-term master key, and the nonce corresponding to that session.

AES will expand its key (128, 192 or 256-bit) to 128-bit subkeys (one more than there are rounds, thus 11, 13, or 15 subkeys), using an algorithm known as the AES key schedule, but that's considered internal to AES.

Notice that any DRBG needs a seed input, and that must be random and secret, thus best generated by a True RNG.



Update following comment: to my knowledge, NIST has no publication fully describing a particular TRNG (which they designate as nondeterministic random number generator); the closest thing (pointed by Thomas M. DuBuisson) seems to be draft NIST SP 800-90B, which gives general recommendations for (mostly: the conditioning of) entropy sources.

NIST does have publications, in particular FIPS 140-2, on how a TRNG should be tested (both during use and for certification purpose) and used; quoting that (as current in 2003):


  Until such time as an Approved nondeterministic RNG standard exists, nondeterministic RNGs approved for use in classified applications may be used for key generation or to seed Approved deterministic RNGs used in key generation. Commercially available nondeterministic RNGs may be used for the purpose of generating seeds for Approved deterministic RNGs. Nondeterministic RNGs shall comply with all applicable RNG requirements of this standard.


Quoting a 2012 draft of annex of FIPS 140-2 annex C on RNGs


  There are no FIPS Approved nondeterministic random number generators.


NIST maintains a list of cryptographic devices with a certificate made in relation to the aforementioned publications.