What message does the picture of Lord Shiva convey?

Vedic Masters used stories and symbols to convey Maha Tattva, the great message conveyed by the Vedas and Vedic Philosophy.

In the picture, Lord Shiva is normally seen in a fully squatting posture with folded hands where the back of the palm of one hand is resting on the palm of the other hand, eyes closed and seen meditating with extreme concentration, completely impervious and oblivious to the external world.

The direct message Lord Shiva trying to give us is urging us also to Meditate.

Meditate on what?

Meditate, concentrate, contemplate on the fact that I am a nameless, formless, Concentrating Entity, Consciousness, Awareness, Knowingness, Chit Shakti (Sentient Energy), Atman (Self).

To know exactly how to do the meditation please see my answer to the question How can I attain self-realization according to Ramana Maharshi?

What is conveyed by the snake coiled around the neck of Lord Shiva?

The hood of the snake is very still and the snake is highly alert. It signifies the state of a very still and highly alert mind. It is this state we are supposed to reach by the meditation. Still mind means mind without any thought or with only one thought which is "I am a nameless, formless, Concentrating Entity, Consciousness, Awareness, Knowingness, Chit Shakti (Sentient Energy), Atman (Self)". Alert mind means 100% concentration, highly focused single pointed concentration, full of Awareness, Pure Consciousness.

Why Lord Shiva has ash smeared on the forehead and all over the body?

Anything when burnt fully it becomes ash. But we cannot burn ash. We cannot destroy ash. Hence it is indestructible. This indestructible ash is used by Lord Shiva to symbolise our indestructible Atman (Self), Chit Shakti (Sentient Energy).

Is this something we need to believe blindly?

This is not belief but Pure Science. I deliberately used the word Shakti (Energy) and the same exact word is used in Svetasvatara Upanishad (1.3) and Kaivalya Upanishad (1.21). According to the First Law of Thermodynamics "Energy can neither be created nor destroyed" which means any Energy is eternal. This is exactly what Lord Shiva is conveying through indestructible ash that the Atma Shakti which is powering each one of us is indestructible and eternal. The mistake lies with we limited individuals who wrongly identify "I" with our name, body and mind. Through ash, Lord Shiva is telling us to correctly identify "I" with the indestructible Atman (Self).

Why Lord Shiva smears the ash as a set of three stripes on the forehead and all over the body?

For this we need to understand a Sanskrit word "Triputi" meaning Triad, set of three. Whenever we observe something there is "Observer" (Pramaata), "Observation" (Pramaanam) and the "Observed" (Prameyam). Any kind of knowledge we gain using our intellect, the Triputi is always present. Seer-Seeing-Seen (Drig Drishya Viveka), Concentrating Entity-Concentration-Concentrated (object), Cognizer-Cognizing-Cognized, Thinker-Thinking-Thought, Knower-Knowing-Known, etc.

Every single knowledge we have gained always involved the Triputi, Knower-Knowing-Known. The Knower which is "I" is always distinct and different from the act of knowing and the known (object or concept). Therefore "I" is the "Subject" and the known is the "Object", the Subject is always different from the Object and hence all the knowledge that we gain using our mind or intellect is called "Objective Knowledge".

There are certain knowledge which cannot be gained by just hearing or reading and may require practice and actual experience. For example, the knowledge of joy, pain, sorrow, love, anger and all other emotional feelings cannot be read and understood but have to be experienced. The knowledge of driving, welding, machining, tailoring, cooking, surgery, playing, etc. cannot be read and understood but have to be practiced and experienced. Such kind of knowledge that can be had only after experiencing it is called "Experiential Knowledge". Even such Experiential Knowledge also involves Triputi. For example, in case of driving there is Driver-Driving-Driven. Thus there is a Subject and Object and hence this kind of knowledge is also "Objective Knowledge".

By meditation we are trying to Know the Knower. But there are no two Knowers so that one could try to Know the other. There is only one Knower and now the task is one has to know oneself. Thus there is only "Subject" and there is no "Object" and hence the Knowledge gained by Self-Realisation is called "Subjective Knowledge". Hence the difficulty, because we are always used to knowing "Objective Knowledge". To gain this "Subjective Knowledge" one cannot know using the intellect but one can gain the knowledge through Aparoksha Anubhuti (Direct Experience) by experiencing by "being" or "existing" as a nameless, formless, Concentrating Entity, Consciousness, Awareness, Knowingness, Chit Shakti (Sentient Energy), Atman (Self).

When we simply exist as a Knower, the Triputi gets merged into one as there is no act of Knowing and there is no external thing called as Known. There is just one pure Knower. That’s all.

To merge Triputi into one, to transcend Triputi, Lord Shiva smears the ash as set of three stripes.

There are also other sets of three Lord Shiva wants us to transcend. Some of them are given below.

Past-Present-Future (Trikala, three times)

Satwa-Rajas-Tamas (Three Gunas or Qualities)

Jagrat-Swapna-Sushupti (Waking-Dream-Deep Sleep)

Vishwa-Taijasa-Pragna (Names of the Consciousness in Waking-Dream-Deep Sleep)

Sthoola-Sukshma-Kaarana Shariras (Gross-Subtle-Causal Bodies)

Tat-Twam-Asi (Three words, Thou Art That)

A-U-M (Three letters of Omkara)

Does any energy such as Gravitational Energy has past, present and future? In the same way when we exist as energy, Concentrating Energy, Chit Shakti (Sentient Energy) we automatically transcend all the sets of three mentioned above. All the triads lose their meaning. Lord Shiva is urging us to determinedly engage in meditation and transcend the triads. Hence the ash is smeared as set of three stripes.

Why Lord Shiva sits in Smashana (Graveyard)?

Lord Shiva is the greatest of the Self-Realised. For him, heaven or graveyard does not make a difference. He is blissful in existing as Chit Shakti (Sentient Energy) and no more joy or sorrow can touch him. Lord Shiva is extremely comfortable sitting in the graveyard without any trace of fear or disgust.

"Fear of Death" is the greatest fear every human being has. Lord Shiva is comforting us not to fear death and reminding us to realize that we are eternal if we successfully identify ourselves with the eternal energy, Atma Shakti (Self).

Lord Shiva by sitting in the graveyard is conveying that this is where the body ends. Hence he is hinting us not to identify with the body or its name and exist as limited individuals, instead identify with the unchanging, undecaying (inexhaustible), eternal Energy which is Atma Shakti, Consciousness, Awareness.

You might also be interested in reading my answer to the question What message does the picture of Lord Ranganatha convey?

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