For English loanwords, there are a couple signs:
-if there are a lot of "hard/aspirated" consonants in the word. In Korean, the "hard" consonants most closely resemble most of the corresponding consonants in English, so coffee is "커피", with the "ㅋ" and "ㅍ" being the hard/aspirated counterparts of "ㄱ" and "ㅂ". And additionally, Koreans don't have an "F" letter or sound, so the "F" sound in coffee is represented with the aspirated "ㅍ" letter instead.
-In Korean, consonants at the end of words are not distinctly pronounced, unless they are followed by vowels. So, "맛" is spelled with the characters "m+a+s" but is pronounced more like "m+a+t" with the t at the end not strongly/thoroughly pronounced. However, in English loanwords, the "으" vowel is added onto words that end in a consonant in order to replicate our more drawn-out pronunciation of these ending consonants. So, "Christmas" would be "크리스마스", with the "s" at the end represented as "스", or "su" in order to draw the sound out more like english pronunciation. This is also why Korean (and Japanese) learners of English often add "u" or "으" sounds at the end of words.
For Hanja, it would be quite difficult to recognize them without some existing knowledge of another sinitic language, such as Mandarin, Cantonese, or (peripherally) Japanese. Years ago, before I learned any Cantonese, I had very little luck in learning Hanja, and it seemed counterproductive to do so, especially given how simple/easy to read Hangul is compared to Hanja. However, after learning Cantonese (and some Japanese) I found that just by hearing/reading the pronunciation of many words I could recognize them as Hanja-based, given their similarity in phonetics. For example, the word for King, "왕" (wang) is 王 (wong) in Cantonese, and thus just hearing the Korean word made me think of its Cantonese counterpart, and recognize it as Hanja. Also, most legitimate Korean-English dictionaries will have the Hanja next to the Hangul for each words if they are of sinitic origin, another good thing to pay attention to when looking words up.