In meditation circles we talk a lot about mindfulness, non-judgemental awareness, and letting things be as they are. This is a beautiful practice that can bring about a great deal of freedom and joy. For some people, though, it can be more helpful to cultivate beautiful qualities of the heart and mind directly. Fortunately, there are meditation practices which do just this.
For millennia, meditation practitioners have worked to cultivate four beneficial attributes in particular, sometimes called the 'four immeasurables' because of their priceless value. Since these practices have a long tradition behind them, you'll sometimes find them called by their Pali names. (Pali is an ancient language related to Sanskrit, and is the language of the teachings of early Buddhism.)
There are various ways to cultivate these qualities in meditation. One approach is to repeat certain phrases silently to ourselves in meditation: 'may this person be happy, may this person be free from suffering'. People who are more visual tend to prefer visualisations, such as imagining a golden light shining in your heart and radiating out to touch other people. Some people simply tap into a physical sense of these qualities in the body and stay with that feeling, allowing it to grow and develop over time like a carefully tended garden.
It's worth saying that, for some people, these practices can be surprisingly difficult. For some people it can feel cheesy or inauthentic to try to cultivate kindness towards someone if they don't already feel it. If this is you, that's absolutely fine - it doesn't make you a bad person! You might try giving it another go in six months (or six years!) to see if anything has shifted, but in the meantime you're much better served finding a different practice that works better for you personally. Meditation is one of the most personal activities you will ever undertake, so it's important to be honest with yourself about what you get on with rather than forcing yourself to do something you don't like because you think you 'should' do it.
One more note of caution: many people in our society already give a tremendous amount of their time, energy and love in the service of others. Occasionally, these practices can end up as a guilt trip - 'Oh, I need to give even more compassion to other people instead of taking a holiday and looking after myself!' If you're one of these people, I strongly suggest you start with loving kindness and compassion for yourself. To put it another way, put on your own oxygen mask first!
If you'd like to try out these practices, you'll find some guided meditations in the Audio section of this website. There are two each for loving kindness and compassion: one for people who are primarily auditory, using the phrases, and one for people who are primarily visual, using a golden light visualisation. If you are primarily kinesthetic, and prefer to work simply with a physical feeling of love or compassion, I suggest using the guided audio with phrases, and treat the phrases as reminders to keep checking in with that felt sense of kindness or compassion.