A common meditation technique that has been passed down through the millennia is Loving Kindness or Metta Bhavana meditation.
There is a reason it has stood the test of time: it works. One study done at Stanford University suggests that a loving-kindness meditation practiced even for 7 minutes can increase social connectedness. Loving kindness meditation has also been shown to help people with chronic lower back pain and Researchers at the University of North Carolina at Chapel Hill demonstrated that loving-kindness meditation can help increase positive emotions.
The actual technique has many variations but they generally start by you finding a quiet place, assuming a comfortable seated position, closing your eyes and setting for your self a period of time to do the practice. Once you are ready, a common way the practice is done is that you begin by visualizing someone for whom you have positive feelings (like a teacher or benefactor) and then you simply repeat phrases of good will (e.g. "may you be peaceful, may you be free from suffering, may you be healthy") directed towards that person. Next you visualize a friend and repeat the process of directing the loving and kind feelings towards them/their image in your mind's eye. Then you do the same thing with someone who is neutral, then someone who is difficult for you, then to all sentient beings, and finally to all things in the universe.
The Vietnamese Buddhist monk Thich Nhat Hanh's version of Metta is as follows:
We begin practicing this love meditation on ourselves
May I be peaceful, happy and light in body and spirit.
May I be safe and free from injury.
May I be free from anger, afflictions, fear and anxiety.
After that we can practice on others (he/she)
May he/she be peaceful, happy and light in body and spirit.
May he/she be safe and free from injury.
May he/she be free from anger, afflictions, fear and anxiety.
After that we can practice including ourselves with others (we),
May we be peaceful, happy and light in body and spirit.
May we be safe and free from injury.
May we be free from anger, afflictions, fear and anxiety.
Each person can develop their own version. For example, you could start with yourself, then go to loved ones, especially those who are suffering, then to friends, acquaintances, mentors, then out to neutral strangers, enemies or criminals/dictators, then to all beings, etc. then back through the list again in reverse to yourself if there is time. You can repeat it over and over with your full concentration on generating the feelings and imaging the people for however many minutes you can manage as many times as feels right each day. And you can adapt it to what seems to fit for you or for that day.
Another variation you could try:
May I be filled with lovingkindness
May I be peaceful and at ease
May I be safe and protected
May I be healthy and strong
May I be resiliently happy
Then cycle back through these five phrases replacing the "I" with (for example) a friend, then someone neutral, then someone negative, then all sentient beings, then, if there is time, back through the list to yourself, then back out again and so on.
 Chapter 5 of No Mud, No Lotus: The Art of Transforming Suffering By Thich Nhat Hanh