Namo Shani devyaa

namo Martandam suputram balishtham,
namo Chaya taatam harantam arishtam'
namo Raudra roopam,anoopam akhandam'
namo moath vabhru namo sauri chandam!

Start your Saturday by offering clean water to the sacred Peepal tree, and chant any mantra/ chalisa referring to Lord Shani dev. It can be- ऊ शत्रो देवीरभिष्ट आहो भवन्तु पीतये।
शं योरभिःस्त्रवन्तु नः॥

or

Pingal Krishno Chaya nandan, Yam kaunastha raudra dukh bhanjan

or it can be the above 4 lines!

What is being said here is that offering our respects to Lord Saturn/ Shani in the morning, by remembering him wholeheartedly, is an auspicious way to start the day. Later in the day, you can do the jaap of Mahamritunjay too, since Lord Shani and Lord Shiva are close to each other. Hence,worshipping Lord Shiva is beneficial too.  'Mreityunjay Mahadev traahima sharanaagatam, 

janam mritu jada vyadhi peeditam karam bandhanai:

 Om Trayambakam Yajamahey, sugandhim pushtivardhanam,

 urvaaruka meev bandhanaan, mrityur mukshiya maamrataat. Om!'

Similarly reciting the Hanauman Chalisa on Saturday too is beneficial for individuals.

Hanuman Chalisa Doha
Shri Guru Charan Sarooja-raj Nija manu Mukura Sudhaari
Baranau Rahubhara Bimala Yasha Jo Dayaka Phala Chari
Budhee-Heen Thanu Jannikay Sumirow Pavana Kumara
Bala-Budhee Vidya Dehoo Mohee Harahu Kalesha VikaaraChopai
Jai Hanuman gyan gun sagar
Jai Kapis tihun lok ujagarRam doot atulit bal dhama
Anjaani-putra Pavan sut namaMahabir Bikram Bajrangi
Kumati nivar sumati Ke sangiKanchan varan viraj subesa
Kanan Kundal Kunchit KeshaHath Vajra Aur Dhuvaje Viraje
Kaandhe moonj janehu sajaiSankar suvan kesri Nandan
Tej prataap maha jag vandanVidyavaan guni ati chatur
Ram kaj karibe ko aaturPrabu charitra sunibe-ko rasiya
Ram Lakhan Sita man BasiyaSukshma roop dhari Siyahi dikhava
Vikat roop dhari lank jaravaBhima roop dhari asur sanghare
Ramachandra ke kaj sanvareLaye Sanjivan Lakhan Jiyaye
Shri Raghuvir Harashi ur layeRaghupati Kinhi bahut badai
Tum mam priye Bharat-hi-sam bhaiSahas badan tumharo yash gaave
Asa-kahi Shripati kanth lagaaveSankadhik Brahmaadi Muneesa
Narad-Sarad sahit AheesaYam Kuber Digpaal Jahan te
Kavi kovid kahi sake kahan teTum upkar Sugreevahin keenha
Ram milaye rajpad deenhaTumharo mantra Vibheeshan maana
Lankeshwar Bhaye Sub jag janaYug sahastra jojan par Bhanu
Leelyo tahi madhur phal januPrabhu mudrika meli mukh mahee
Jaladhi langhi gaye achraj naheeDurgaam kaj jagath ke jete
Sugam anugraha tumhre teteRam dwaare tum rakhvare
Hoat na agya binu paisareSub sukh lahae tumhari sar na
Tum rakshak kahu ko dar naaAapan tej samharo aapai
Teenhon lok hank te kanpaiBhoot pisaach Nikat nahin aavai
Mahavir jab naam sunavaeNase rog harae sab peera
Japat nirantar Hanumant beeraSankat se Hanuman chudavae
Man Karam Vachan dyan jo lavaiSab par Ram tapasvee raja
Tin ke kaj sakal Tum sajaAur manorath jo koi lavai
Sohi amit jeevan phal pavaiCharon Yug partap tumhara
Hai persidh jagat ujiyaraSadhu Sant ke tum Rakhware
Asur nikandan Ram dulhareAshta-sidhi nav nidhi ke dhata
As-var deen Janki mataRam rasayan tumhare pasa
Sada raho Raghupati ke dasaTumhare bhajan Ram ko pavai
Janam-janam ke dukh bisraavaiAnth-kaal Raghuvir pur jayee
Jahan janam Hari-Bakht KahayeeAur Devta Chit na dharehi
Hanumanth se hi sarve sukh karehiSankat kate-mite sab peera
Jo sumirai Hanumat BalbeeraJai Jai Jai Hanuman Gosahin
Kripa Karahu Gurudev ki nyahinJo sat bar path kare kohi
Chutehi bandhi maha sukh hohiJo yah padhe Hanuman Chalisa
Hoye siddhi sakhi GaureesaTulsidas sada hari chera
Keejai Nath Hridaye mein deraDoha
Pavan Tanay Sankat Harana 
Mangala Murati Roop
Ram Lakhana Sita Sahita 
Hriday Basahu Soor Bhoop

JAI SHANI DEV KI!!