/ʌ/ cut, hut, bun, nothing, love, enough, flood, does
/ʊ/ put, soot, foot, good, look, cook
/ʌ/ sound is very similar to /ə/ sound (schwa). The only difference is that /ʌ/ occurs in syllables that are stressed while /ə/ occurs in syllables that are unstressed.
/ʌ/ is called Open-mid back unrounded vowel. In order to produce /ʌ/ sound, slightly open your mouth (don't stretch out your lips much otherwise you'll be producing /æ/ sound rather than /ʌ/) and drop your jaw ever so slightly, place your tongue between the middle and the back of your mouth. Press down the back of the tongue a little bit and put the tip of your tongue forward (do not touch the top of the mouth) and produce a vowel sound with your mouth. That's /ʌ/ sound.
Examples: But, run, strut, flood, love, luck etc. -> /ʌ/
/ʊ/ are /u:/ are similar but /u:/ is longer than /ʊ/.
/ʊ/ is called Near-close back rounded vowel.
In order to make /ʊ/ sound, the corners of the lips come in a little (not too much rounded otherwise you'll be producing /u:/ sound rather than /ʊ/) so the lips flare away from the face, the back of the tongue lifts towards the back of the roof of the mouth, the front of the tongue remains down but it miht be pulled slightly back so it's not touching the bottom teeth. That's /ʊ/ sound.
Examples: Book, foot, put, look etc. -> /ʊ/
In Southern British accent (standard or queen's accent), both /ʊ/ and /ʌ/ are pronounced differently (as I explained above). However, in Northern British accents/ dialects (such as Yorkshire, Manchester, Cumbria), they may be pronounced as /ʊ/. ->>> Click here
This phenomena is called strut-foot merger or cut-foot merger and it is one of the main feature of Northern accents.
So those who have strut-foot merger might pronounce strut and foot with the same vowel sound (/ʊ/).
Luck and look the same. Cut and foot etc...
In Northern England and Scotland, as well as some dialects in Ireland, the vowels in FOOT is the same as the vowel in STRUT and FLOOD. Liverpool speakers would pronounce the vowel in FLOOD, RUN and SUN the same way they pronounce it in HOOD, FOOT, and BOOK.
Here's a good explanation about Strut-Foot split in linguistics SE: Link (second answer)
For me, the difference between the two vowel sounds is subtle. You will just need to practise a lot.
(In Game of Thrones, some characters like Ser Devos, Jon Snow, Ygritte, Ned Stark have Northern accents which means they pronounce /ʌ/ and /ʊ/ the same way).
Click here to see how they are articulated. (Sorry, there is no direct link to either of the vowel. Click on the link then; vowels -> monopthongs -> select central for /ʌ/ and back for /ʊ/)