There are two practices that have served me greatly and I highly recommend. The two audio recordings below will get you started.
Before you start you will need to set up your seated position. The hips should be above the knees, using cushions to prop them up. You can straddle the cushions or sit in easy pose (Sukhasana). The palms can face up with the right palm over the left and the thumbs lightly touching or palms facing down resting on the knees.
For those who cannot sit like this for an extended period of time, sitting in a chair is also an option. Unless you are in pain from sitting, it is advisable to move as little as possible so as to focus on the practice.
The Mindfulness of Breathing
Using the breath as a point of concentration there are four stages; counting up to ten after every exhalation and then starting again at one, counting up to ten after every inhalation and then starting again at one, dropping the count in the third stage and just watching the breath, and the final stage focussing on the tip of the nose when the breath first enters and leaves the body.
When your mind starts to wander – and it will, simply return to the breath. Normal, easy breathing without judgement, simply observing and being a witness to the breath.
More on the mindfulness of breathing.
The Metta Bhavana
In English, the Metta Bhavana translates to Loving-Kindness in a non romantic way. There are five stages; firstly focussing on yourself using the phrase of ‘may I be happy, may I be well, may I be free suffering’, the second stage focussing on a good friend using the same phrase above, the third stage using the same phrase thinking of someone you don’t particularly know and are neutral too, the fourth stage focus on someone you don’t like, and the final stage think of all the four people and start to expand it to include the world.