For anyone who know's someone who is lonely, it's important to know that being supportive involves getting the right balance; understanding and accepting how the other person is feeling but without getting too caught up in their situation and feeling solely responsible for easing their loneliness.
Think of interesting, relaxing and / or fun things you can do together. Offer to accompany the other person to appointments they may have.
Talk with the other person about what they want and need in terms social contact with others and what sort of social activities they might like to join in with.
Help them to research what activities - Meetup groups, classes and courses, and / or voluntary opportunities are available. Also, help find out what services, support and information is available.
Encourage the other person to commit to specific actions - one step at a time - so that they can help themselves and move forward. Once they’ve identified something to aim for, do be positive and encouraging.
Don't push them into situations that may be too much to handle. Let the person decide how much or how little they feel comfortable with, but always encourage them to move forward.
If they're resistant, find out what their concerns are. Acknowledge - don't dismiss - the challenges but remind them of their reason to connect with other people; what they’ll gain, how they’ll improve their situation.
Going to things alone - especially for the first time - is not easy. You, another friend or family member could go to something with them for the first time.
Reassure them that it can take time and effort to feel less lonely and that they shouldn’t be disheartened if things aren't moving at the pace they'd like it to.