Dear Sri Pragasen Chetty
Please let me try to help you in your efforts to find the "proper cleansing ritual before meditating on Bhagavaan Lord Naaraayana", one of our Thri-Moorthies.
Hindus normally take a whole-body bath or shower (including washing hair on head) first, then change into underwear (or loin-cloth called kaupeenam), wear a wrap-around piece of cloth round the waist reaching down to the ankles, and tie/knot a cummerbund or belt-like piece of smaller second cloth around the waist. You can be bare-bodied (preferred), or wear a singlet or t-shirt if more comfortable.
Next, place a small mark in the centre of your forehead with sandalwood paste and/or reddened turmeric powder. Use sacred ash if you do not have sandalwood paste or reddened turmeric powder.
Find a quiet, clean spot, preferably not too dark or lit blazingly bright, away from distractions, and sit comfortably on the ground on a small mat, a small piece of carpet, or a slightly-raised plank.
If you know and can assume the lotus posture, so much the better. If not, just relax. If you can only sit relaxed on a chair or stool or swing, do so. Do not sit on a pillow, a cushion, a mattress, or a bed. Sit preferably facing east or north. Never face south (that direction is for honouring spirits of dead ancestors).
Now, let me take you through the motions of the aachamaneeyam, which is the preliminary requisite part of the worship of Lord Naaraayana (as well of Lord Shiva and of all other Hindu gods and goddesses).
(1) Close your right hand into a fist, stick out your right-hand thumb, touch your right cheek with the tip of your right thumb. Say "KESAVA".
(2) Touch your left cheek with the tip of your extended right thumb. Say "NAARAAYANA".
(3) Touch the closed eyelid of your right eye with the tip of your right-hand ring finger (next to your little finger). Say "MAADHAVA".
(4) Touch the closed eyelid of your left eye with the tip of your right-hand ring finger (next to your little finger). Say "GOVINDA".
(5) Touch the upper part of your right nostril with your right index finger. Say "VISHNU".
(6) Touch the upper part of your left nostril with your right index finger. Say "MADHU-SOODHANA".
(7) Touch your right ear with your right little finger. Say "TRI-VIKRAMA".
(8) Touch your left ear with your right little finger. Say "VAAMANA".
(9) Touch your right shoulder with your right middle finger. Say "SREEDHARA".
(10) Touch your left shoulder with your right middle finger. Say "HRISHI-KESHA".
(11) Touch your navel with all fingers of your right-hand closed like a lotus bud.
Say "PADMA-NAABHA".
(12) Touch your the top of your head with all fingers of your right-hand closed like a lotus bud. Say "DAAMO-DARA".
That completes the aachamaneeyam.
Now for the japam and meditation.
Practise saying quietly the nine-syllable manthram (ashtaakshara mahaa manthram):-
"OM NAMO NAARAAYA-NAAYA"
Either close your eyes, or have a little lit oil lamp with a small steady flame in front of you to aid you in concentration. Or have a small picture of Mahaa-Vishnu in the form of Guruvaayoor-appan or of Lord Krishna to help you focus. If not, it doesn't matter. Just close your eyes and repeat the manthram slowly and wuietly as many times as you can -- 18, 27, 36, 54, 108.
When done, rise and make a prostration before the lit lamp or sacred picture. Or, if that is too difficult, just clasp your joined palms together, bow your head. Snuff out the flame of the lamp with a flower.
May Lord Sree Naaraayana bless you and protect you.