bhakti

Anugraham (bestowing grace) is one of the fundamental characteristic of Lord Shiva. So, Lord Shiva certainly grants wishes. In the scripture also we find many many stories where Lord Shiva grants wishes to his devotees. Like giving son to Vyasa, Sanjivani Vidya to Sukra, Drinking poison on request by Devas, Giving Chandrahaans to Ravana etc... and so on. YajurVeda also after the Rudram section asks of many desires from it's Chamakam section. Similarly the Upanishads also speak the same. Eg. Svetasvatara Upanishad 6.13 states:

नित्यो नित्यानां चेतनश्चेतनाना-                मेको बहूनां यो विदधाति कामान् । तत्कारणं सांख्ययोगाधिगम्यं                ज्ञात्वा देवं मुच्यते सर्वपाशैः ॥ १३॥

He is the Eternal among the eternal, the Conscious among the conscious and though non-dual, fulfils the desires of many. He who has known Him, the luminous Lord, the Great Cause, to be realised by Knowledge and yoga, is freed from all fetters.

So, the thing is doing various methods so that Lord Shiva graces us. There are various methods provided in Puranas like Shiva Purana and Linga Purana which can be used to obtain various desires. Like;

1) Performing ShivaLinga Abhisekam 2) Performing Sri Rudram Homam 3) Performing MahaMrityunjaya Yajnam etc...

These all methods should be done as per the methods given in Puranas and with the help of a good Priest.

There are also Nãma-Japa methods which can be used to invoke Grace of Lord Shiva. The most special is Shivas eight name which are very much emphasized in Vedas and Puranas. The eight names are:

● रुद्र (Rudra) ● भव (Bhava) ● सर्व (Sarva) ● ईशान (Ishana) ● पशुपति (Pashupati) ● भीम (Bhima) ● उग्र (Ugra) ● महादेव (Mahadeva)

These Eight names of Lord Shiva are very beneficial and chanting them can invoke grace of Lord Shiva. There are also five names which are also verified by Vedas:

● रुद्र (Rudra) ● भव (Bhava) ● सर्व (Sarva) ● शिव (Shiva) ● मृड (Mrida)

Chanting of these five names can also invoke grace of Lord Shiva. Similarly, chanting of the name 'Shiva' is also highly emphasized in Shiva Purana. Hearing of stories related to Lord Shiva can also invoke grace of Shiva. And the Panchakshari Mantra 'Om Namaha Shivãya' though seems simple is highly potent and the most emphasized mantra in Shiva and Linga Purana.

As a sidenote I discuss in my answer here various mantras which can be used to worship Lord Shiva.