Saucha - purity 
This refers not just to external cleanliness but also clean/pure attitude, mind and behaviour eg. physically (asana and diet), emotionally (breath awareness when stressed/tired/angry can break negative patterns of behaviour) and mentally (meditation helps deepen our Self awareness and gain control of our mind rather than allowing our perception and emotion to lead our mind).  Saucha is when we cleanse our whole Self, letting go of impurities in body, mind and spirit, the things that hold us back from being all that we can be. We can use awareness to watch our thoughts etc and change negative ways of thnking, acting, speaking.

Santosha - contentment
Accepting our Self and the universe as it is rather than having expectations and a perception of how it should be or how we would like it to be.  Accepting where we are, what we are and what we have for what it is without being attached to dreams, desires & expectations.  Letting go of these ideals and making choices around what is on offer without trying to change it.  It is our attitude we change from negative to positive.  We stop wanting and accumulating which frees us.

Tapas - self discipline
This can be interpreted as how much energy and fire we are prepared to put in to our goal.  The will-power and fire that will burn up any obstacle in our way.  It is what motivates us to put in the ongoing commitment/effort towards a purpose which the sankalpa (positive affirmation) helps us achieve.  We will still have ups and downs but the regular effort will lead us on the right path towards our goal and so there will be less suffering.

Svadhyana - self-study
Learning about our strengths, weaknesses, needs and what motivates us. Finding out patterns of behaviour and turning them into positive patterns so our weaknesses become strengths.  Sometimes we don't like what we see, it can be challenging to realise yet important to accept our Self 'warts and all' is what we need to do to manage these weaknesses without allowing them to trip us up. When we 'see' our weaknesses, they loose their power over us.  As we become more Self-accepting we judge our Self and others less and find our hearts opening up.

Ishvara-pranidhana - surrender
Letting go of trying to control where we end up and the end result, fruits of our actions.  By surrendering to the journey we are in the present and still able to choose our response to a situation we are face with. By being increasingly present and aware, we are trusting that this path will lead us to where we need to be rather than towards where we think want to be.  Expressing our Self through the journey and trusting that this will lead us to fulfilling our purpose and living a full life towards achieving our potential.  Having faith in our Self and that there is something greater than our current life experience.

Yoga helps us to move towards these aspirations without being too hard and trying to go from A-Z too quickly.  Everything in moderation, don't be too hard on yourself either which is why it's under love and laughter - it's not about self-flaggelation (beating ourself up for not being perfect)!  It's about moving forward on your journey and purifying along the way even if occasionally we take a step or two back! 

Yamas & Niyamas are derived from Raja yoga (by the sage Patanjali).  They are comprised of social & personal guidelines which instil a sense of peace and clarity into one's life and avoid mental disturbance and confusion.  It is useful practice to choose one of these to focus on for the day.  

Yamas - Guidelines for harmoniously interaction with our external environment
Ahimsa - non violence
Being positive in our actions, thoughts, words towards ourselves & others.  Being kind towards ourselves and others.
Satya - truth
Living and expression our true nature. Saying what we really mean, acting in a way that is true to our Self.  Even thoughts are tinged with doubt stemming from insecurities and past experience and can change the way we think, act, feel and speak, creating negative patterns.  Try to first notice a behavioural pattern and then it will gradually loose it's power as you identify it and attempt to turn it into a truthful expression of your Self.
Asteya - honesty
This is about being truthful and accepting of where we are at without trying to represent our Self as something we are not and in the process causing harm to our Self and others.  Being truthful including not mis-leading.
Brahmacharya - restraint
Moderation of sensual desires including foods, drink, intimate relations whilst practicing the other yamas so as not to cause any harm to the self or others as they are all inter-related.  So using the higher mind and awareness so we are in control of our actions/decisions instead of being led by our cravings.
Aparigraha - not wanting what others have
Only taking what is needed and not longing for more.  Not being greedy, jealous and envious and attached to material objects and our perception of who we/others are etc.  If we give up wanting what other people have we become so much freer and independent of them, not relying on them for our happiness.  It is good to care for what we have and look after it but not with attachment.

A sankalpa (ancient language meaning 'affirmation') is a resolve or goal.  A sankalpa should be a short, positive statement "I will....." rather than "I wont....".  A realistic goal or aim which you are striving for but obstacles of life are holding you back.  This goal should remain the same and not be changed until it has been acheived when the time is right.  The more one thinks about it and waters this seed they have planted in their mind, the stronger the will behind it and so the more energy is put into transforming this idea/seed into reality.  It can be anything, health, spiritual or even overcoming an obstacle or achieving something important to you.  Use it regularly and you will see how the mind becomes more focused and aware of opportunities that help you reach this goal!  

A Sankalpa is used in Yoga nidra at the start and end of the practice when the mind is relaxed and more receptive.  It should be kept private and thought about in every day life too especially upon waking and before sleep.