I'm lonely
Use this to say 'I feel lonely.' It's very common and clearly expresses the emotion, rather than just the state of being physically alone.
A softer way to say you're lonely, translating to 'I need/miss company.' It's a good way to invite someone to spend time with you.
This means 'I miss my friends.' It's an indirect way to express loneliness by stating the reason for it.
I didn't leave the house today and now I'm a little lonely.
Sometimes I feel lonely in this new city.
I'm feeling lonely. Do you want to get coffee later?
It's my first day here and I feel a bit lonely.
Both 'Estoy solo/a' and 'Me siento solo/a' are universally understood and used. 'Me siento solo/a' is often preferred to specifically mean 'I feel lonely' as an emotion.
Usage is identical to Latin America. 'Estoy solo/a' and 'Me siento solo/a' are the standard phrases.
It's common to add 're' as an intensifier, as in 'Estoy re solo' or 'Me siento re sola,' which means 'I'm super lonely.'
While the standard phrases are common, you might also hear 'Me siento agüitado/a' (I feel down/bummed out), which can imply loneliness.
Using 'ser' instead of 'estar'. Saying 'Soy solo/a' means 'I am a solitary person' (a personality trait) or that you're single, not that you are currently feeling lonely. The correct verb for a temporary feeling or state is 'estar': 'Estoy solo/a'. — Estoy solo/a.
Forgetting gender agreement. The adjective 'solo' must match the gender of the person. A man says 'Estoy solo,' and a woman says 'Estoy sola.' — A man says 'solo', a woman says 'sola'.
Confusing 'solo' (lonely/alone) with 'único' (only one). If you say 'Soy la única persona aquí', it means 'I'm the only person here.' 'Estoy solo/a' can mean you are physically alone or that you feel lonely. — Use 'Estoy solo/a' for being alone or lonely.