Good Question. A Vaishnava-based answer ahead…
I would tell you as much as I have learnt, and as per my competence. You can do the japa of the Shiva Panchakshari Mantra ‘Om Namah Shivaya’ or just ‘Shiva’, ‘Hara’, ‘Mruda’, ‘Bhava’, ‘Sharva’, ‘Shambhu’. But just doing it mechanically won’t yield you anything. You need to do it with devotion, because Lord Shiva can only be pleased by devotion. Lord Shiva doesn’t see how beautiful you are, how rich you are, but only sees your bhakti. If you have bhakti, then you can please Lord Shiva.
While doing japa, you can remember the great qualities which Lord Shiva possesses and see Him by closing your eyes. His jataa, which is of the color of molten gold and is radiant. He has the moon on His jataa, and Ganga flowing from the jataa. He doesn’t have cleanly combed hair as we see in today’s paintings and pictures, but it is rough and matted.
His hair is flowing down, touching His shoulders. He has 5 faces, namely - Sadyojata, Aghora, Vaamadeva, Ishaana, Tatpurusha. Tatpurusha is the central face, which is of the color of Sphatika. Every head of Lord Shiva is of a different color, namely, yellow gold, sphatika, dark color, ruby red, and cloud grey color. He has three eyes in each face, resembling that of a lotus. He is very handsome. SriVaadiraja Tirtharu describes Lord Shiva as “पार्वती श्लाघ्यवेषः,” which means His roopa is praised and admired by Umadevi.
He has a snake and Rudraakshi maala around His neck. He has applied Bhasma all over His body, which represents His Vairagya or detachment. He doesn’t wish for anything, but He provides everything to His devotees. Umadevi is sitting on His left lap. Remember that Umadevi must always be worshipped with Lord Shiva, because both will be pleased only when they are worshipped together. She also doesn’t have open hair like we see today. Her hair is described as Pannagaveni, which means from the backside if you see, Her hair will look like a snake whose hood is flared, which means She has tied Her hair with a hair bun decorated with fragrant flowers and a long braid. She wears kumkuma tilaka on Her forehead. She is eternally beautiful. She wears a garland of pearls and a mohana maala around Her neck, with a deeply sculpted armlet or upper armband. Her hands are full of sparkling and colorful bangles. She is wearing elegant clothes, with anklets on her feet, which is worshipped by Indra and other devatas with deep devotion.
Lord Shiva, thus always accompanied by Umadevi, is holding the Vara and Abhaya mudras in both His hands, as you can see in the image above of SriUmaMaheshwara. On the other hand, He is holding Trishoola and Damarooka. Sometimes, He is even holding a deer and Damarooka. He has worn Vyaghra charma. Even sometimes He is depicted as Gaja charma dhaari, but He appears in both ways as the devotees see Him. He is sitting in Padmasana. He can only be pleased by Bhakti. See Him with the eyes of Bhakti and do the naama japa.
Do chintana of His qualities, like for example since He is auspicious, He is known as Shiva, He is ever-auspicious, He is known as Sadaashiva, He is known as Sharva, because He is samhaarakarta, and Umadevi is known as Sharvaani because She also does samhaara along with Lord Shiva in Her Durga roopa. He is known as Shambhu because He provides happiness, He is known as Rudra, because He is shatrubhayankara, He is known as Vaamadeva, because He is very handsome. He is known as Kaamaari because He burnt Kaamadeva into ashes, Gowreesha because He is the Lord of Umadevi. He is known as Hara since He removes all our sins, and He is known as Mruda because He provides happiness. He is the guru to Indra and other devatas. They get Shastra abhyasa from Lord Shiva and Shaastra paatha by Umadevi. Lord Shiva and Umadevi together are the bestowers of maangalya.
Satidevi Herself says to Daksha that the two-word name, ‘Shi’ ‘Va’ = ‘Shiva ’, is enough to remove all the sins. Just by chanting His name, all sins are destroyed. He is the presiding deity for the mind. He is Vaishnavottama and chants Rama naama every time, and this is evident from the Puranas themselves. Don’t worship Him like Vrikasura did. As per Srimad Bhagavatam, He asked Lord Shiva for a boon that whosoever’s head he keeps his hands on should burn into ashes. As Lord Shiva said, ‘So be it’, Vrikasura tried to test it on Lord Shiva Himself. It’s not like Lord Shiva couldn’t undo it or make it false, but if He did so, then it would be like He Himself went against His own boon. Then the story is known as to how Lord Shiva approached Lord Vishnu for help, and He assumed the form of a brahmana and deluded Vrikasura and burnt Him into ashes. Worship Lord Shiva not for boons, but for Lord Shiva’s pleasure, for Lord Srihari’s pleasure, because Srihari is immensely pleased if you worship the Vaishnavottama, which is Lord Shiva. Lord Narasimha or Lord Sankarshana is present as the antaryami of Lord Shiva as per Srimad Bhagavatam.
Keeping all this in mind, do the japa of the Shiva mantra or just say ‘Shiva’, ‘Hara’, ‘Mruda’, ‘Bhava’, ‘Sharva’, ‘Shambhu’, ‘Shankara’, ‘Mahadeva’, etc. with devotion. This is all that I said is the way Vaishnavas do the chintana of Lord Shiva. Especially, SriMadhvacharya in His Tantrasara sangraha named grantha instructs us to do the dhyaana of Panchamukha Rudradeva while doing the Shiva Panchakshari japa. This is the chintana of Lord Shiva as per SriMadhva Siddhanta.
[Shiva Dhyana Mantra provided by SriMadhvacharya in His Tantrasara sangraha]
Hope this helps!
Jay SriRam!
SriParvatipate Hara Hara Mahad