The easiest way to learn Kannada for a Malayalee is to stay in some remote area of Karnataka where only Kannada language is spoken.
There are good teaching Kannada language books available in bookstores and online stores like Amazon.
A sincere approach to new language learning will speed up the learning process.
Making friends with Kannadigas who know the language and requesting them to help you correct your mistakes will be of great use to grasp the basics.
Interact more with the Kannada speakers and lose no opportunity to speak to them. This will help you practice your spoken Kannada and you will learn to speak in Kannada in a short span of time.
Regularly watching Kannada TV, Talk Shows, Documentaries, News Channels will not only help you grasp the diction but also help you learn a lot passively within months.
Malayalam and Kannada descended from Proto South Dravidian branch from Dravidian tree. So they are both similar to each other. A Malayali can easily learn Kannada within 6 months if he/she is a keen observer.

Start by identifying cognates available in both the languages and make comparisons about it. As you can see there are sound shifts happening in Kannada w.r.t. Malayalam.
V-B transition
Vaa(വാ) – Baa(ಬಾ) ( Come)
Vere(വേറെ) – Bere(ಬೇರೆ) ( Else)
Veli(വേലി) – Beli(ಬೇಲಿ) (fence)
Vegam(വേഗം) – Bega(ಬೇಗ) ( Faster)
VeLicham(വെളിച്ചം) – BeLaku(ಬೆಳಕು) (Light)
Vaatil(വാതിൽ) – Baagilu(ಬಾಗಿಲು) ( Door)
Vaataka(വാടക) – Baadige(ಬಾಡಿಗೆ) (Rent)
Vaaya(വായ) – Baayi(ಬಾಯಿ) (Mouth)
Viral(വിരൽ) – BeraLu(ಬೆರಳು) (Finger)
Vaazha(വാഴ) – BaaLe(ಬಾಳೆ) (Banana tree)
Villu(വില്ല്) – Billu(ಬಿಲ್ಲು) ( Arrow)
Vidu(വിടൂ) – Bidu(ಬಿಡು) (Leave)
Veta(വേട്ട) – Bete(ಬೇಟೆ) ( Hunt)
Valarccha(വളർച്ച) – BeLavaNige(ಬೆಳವಣಿಗೆ) ( Growth)
VeNNa(വെണ്ണ) – BeNNe(ಬೆಣ್ಣೆ) ( Butter)
Vila(വില) – Bele(ಬೆಲೆ) ( Price)
VeLLa(വെള്ള) – BiLi(ಬಿಳಿ) (White)
VeLLi(വെള്ളി) – BeLLi(ಬೆಳ್ಳಿ) (silver)
Vaalu(വാല്) – Baala(ಬಾಲ) (Tail)
VarNam(വർണം) – BaNNa(ಬಣ್ಣ) ( Colour)

P-H transition
Paalu(പാല്) – Haalu(ಹಾಲು) (Milk)
Pallu(പല്ല്) – Hallu(ಹಲ್ಲು) (Teeth)
Pullu(പുല്ല്) – Hullu(ಹುಲ್ಲು) (Grass)
Palli(പല്ലി) – Halli(ಹಲ್ಲಿ) (Lizard)
PaLLi(പള്ളി) – HaLLi(ಹಳ್ಳಿ) (Village)
Poovu(പൂവ്) – Hoovu(ಹೂವು) (Flower)
PaNam(പണം) – HaNa(ಹಣ) ( Money)
Pazhaya(പഴയ) – HaLe(ಹಳೆ) ( Older)
Putiya(പുതിയ – Hosa(ಹೊಸ) ( Newer)
Poku(പോകൂ) – Hogu(ಹೋಗು) (Go)
Pakal(പകൽ) – Hagalu(ಹಗಲು) ( Day time)
Pala(പല) – Halavu(ಹಲವು) ( many)
Paatt(പാട്ട്) – Haadu(ಹಾಡು) ( Song)
Pazham(പഴം) – HaNNu(ಹಣ್ಣು) ( Fruit)
Peru(പേര്) – Hesaru(ಹೆಸರು) ( Name)
Puzha(പുഴ) – HoLe(ಹೊಳೆ) ( River)
Pashu(പശു) – Hasu(ಹಸು) ( Cow)
Pakshi(പക്ഷി) – Hakki(ಹಕ್ಕಿ) ( Bird)
PuLi(പുളി) – HuLi(ಹುಳಿ) ( Sour)
C-K transition
Chila(ചില) – Kelavu(ಕೆಲವು) ( Some)
Chila samayam can be Kelavu samaya
Cheera(ചീര) – Keera(ಕೀರ) ( Spinach)
Chevi(ചെവി) – Kivi(ಕಿವಿ) ( Ear)
Chuvapp(ചുവപ്പ്) – Kempu(ಕೆಂಪು) ( Red)
Chedi(ചെടി) – Gida(ಗಿಡ) ( Plant)

A-E transition (end part)
Tala(തല) – Tale(ತಲೆ) ( Head)
Mazha(മഴ) – MaLe(ಮಳೆ) ( Rain)
Bhasha( ഭാഷ) – Bhashe(ಭಾಷೆ) (Language)
Vaataka(വാടക) – Baadige(ಬಾಡಿಗೆ) (Rental)
ENNa(എണ്ണ) – ENNe(ಎಣ್ಣೆ) (Oil)
Aaradhana(ആരാധന) – Aaradhane(ಆರಾಧನೆ) ( Worship)
Mula(മുല) – Mole(ಮೊಲೆ) ( Breast)
Mutta(മുട്ട) – Motte(ಮೊಟ್ಟೆ) ( Egg)
Kuda(കുട) – Kode/Chatri(ಕೊಡೆ/ಛತ್ರಿ)( Umbrella)
Aana(ആന) – Aane(ಆನೆ) ( Elephant)
Kutira(കുതിര) – Kudure(ಕುದುರೆ) ( Horse)
Kola(കൊല) – Kole(ಕೊಲೆ) ( Murder)
Kalpana(കൽപന) – Kalpane(ಕಲ್ಪನೆ) ( Order)

Not just with Malayalam, few of the words in Telugu- Kannada shares A-E sound shifts
Jinka(జింక) – Jinke(ಜಿಂಕೆ) (Deer)
Kappa(కప్ప) – Kappe(ಕಪ್ಪೆ) (Frog)
Meka(మేక) – Meke(ಮೇಕೆ) (Goat)
Ninna(నిన్న) – Ninne(ನಿನ್ನೆ) (Yesterday)
Monna(మొన్న) – Monne(ಮೊನ್ನೆ) (Day before yesterday)
Zha-La transition
Mazha(മഴ) – MaLe(ಮಳೆ) (Rain)
Mazhavillu(മഴവില്ല്) – MaLebillu(ಮಳೆಬಿಲ್ಲು) ( Rainbow)
Ezhu(ഏഴ്) – ELu(ಏಳು) ( Seven)
Veezhcha(വീഴ്ച) – BeeLu(ಬೀಳು) ( Fall)
Puzha(പുഴ) – HoLe(ಹೊಳೆ) ( River)

Most of the words in Malayalam ends with the letter M so if you omit that letter it becomes Kannada( more common with Sanskrit shared words). And letter N too. Let’s have a look at the following words.
Aakasam(ആകാശം) – Aakasa(ಆಕಾಶ) ( Sky)
Megham(മേഘം) – Megha(ಮೇಘ) (Cloud)
Nakshatram(നക്ഷത്രം) – Nakshatra (ನಕ್ಷತ್ರ) (Star)
Samayam(സമയം) – Samaya(ಸಮಯ) (Time)
Kopam(കോപം) – Kopa(ಕೋಪ) ( Anger)
Abhiprayam(അഭിപ്രായം) – Abhipraya(ಅಭಿಪ್ರಾಯ) (Opinion)
Loham(ലോഹം) – Loha(ಲೋಹ) ( Metal)
Vruttam(വൃത്തം) – Vrutta(ವೃತ್ತ) (Circle)
Kavacham(കവചം) – Kavacha(ಕವಚ) ( Shield)
Mukham(മുഖം) – Mukha(ಮುಖ) ( Face)
Teerumanam(തീരുമാനം) – Teermana(ತೀರ್ಮಾನ) (Decision)
Maram(മരം) – Mara(ಮರ) ( Tree)
Vaahanam(വാഹനം) – Vaahana(ವಾಹನ) ( Vehicle)
Madhuram(മധുരം) – Madhura(ಮಧುರ) ( Sweet)
Chakram(ചക്രം) – Chakra(ಚಕ್ರ) ( Wheel)
KaLLan(കള്ളൻ) – KaLLa(ಕಳ್ಳ) ( Thief)
Makan(മകൻ) – Maga(ಮಗ) (Son)
Suryan(സൂര്യൻ) – Surya(ಸೂರ್ಯ) (Sun)
Chandran(ചന്ദ്രൻ) – Chandra(ಚಂದ್ರ) (Moon)

And addition of U at the end part in Kannada
Njaan(ഞാൻ) – Naanu(ನಾನು) (I)
Nee(നീ) – Neenu(ನೀನು) (You)
Avan(അവൻ) – Avanu(ಅವನು) (He)
AvaL(അവൾ) – AvaLu(ಅವಳು) (She)
Avar(അവർ) – Avaru(ಅವರು) (They)
Makal(മകൾ) – Magalu(ಮಗಳು) (Daughter)
Makkal(മക്കൾ) – Makkalu(ಮಕ್ಕಳು) (Children)
Meen(മീൻ) – Meenu(ಮೀನು) (Fish)
Kaal(കാൽ) – Kaalu(ಕಾಲು) (Leg)
If you keep these things in mind, understanding Kannada will be much easier.
Many Malayalees in Bangalore are staying at Madiwala and Koramangala. Ask Malayalis living in Karnataka & knowing Kannada to help you from time to time.
Join Kannada learning forums and group on Facebook, Whatsapp etc.
There is a Whatsapp based teaching service called Kannada Gothilla – which I highly recommend. It comes for a small fee.
