Mistakes Lonely People Often Make
Once someone has become socially isolated and down about it, there are some common traps they can fall into which maintain their loneliness:
They hide from the world because they're embarrassed about being lonely and having no life
People who you don't live with really can't tell all that well how much of a social life you have. More than that, even if they do have a hunch that you may not be up to all that much on the weekends, they likely don't judge you too negatively for it. Of course hiding like this is counterproductive because if you want to start getting a social life together, you have to begin putting yourself out there.
Lonely people can also hide in the sense that they're really guarded about revealing anything about themselves, because someone might catch on to how little they have going on in their lives. Doing this can prevent new relationships from getting off the ground. A lonely person may 'save face' by avoiding a potential new friend, rather than have to reveal they don't have a ton of buddies at the moment.
The alternative is to be more casual and straightforward about the fact that your social life is lacking at the moment. It's actually something that can happen to anyone from time to time. If the topic comes up, you can just say something like, "I've been working too much lately. I've got to start going out more" or "Ha ha, I think I'm in a bit of a social rut at the moment. I fell out of touch with some old friends, and really should start meeting some new people."
They become experts at distracting themselves from their loneliness
It's relatively easy to occupy spare hours in front of a TV, computer, or video game console. Some people even use alcohol or dope to take the edge off. People can also get good at structuring the times they do routine errands, so it almost feels like they're busy and have a lot on the go. Obviously this doesn't do anything to fix the underlying problem.
They get too comfortable in their rut
When your social life isn't where you want it to be you can find yourself in a situation where you wish it was better, but at the same time you're used to things how they are now. Like the point above mentions, maybe you've gotten really good at filling your time with things that are a half-decent substitute for socializing. Being comfortable like this can be insidious in that on some level you want to improve your situation, but you're not feeling enough of a push to really go after it. It's easier to stay in for another weekend and download that new indie game you've heard good things about.
They expect other people take all the initiative in inviting them out
Sometimes you'll meet someone you get along with and they'll make all the effort of getting your contact information and inviting you out, but often this doesn't happen. People are usually pretty busy and already have social lives of their own. They're often on a kind of autopilot where they won't think of you as a potential buddy unless you get them thinking that way. Showing an interest in spending time with them is one way you can do that. By waiting for them to extend you an invitation, and doing nothing to put yourself on the line, you may have been unwittingly implying that you weren't interested in hanging out with them.
Also, lonely people can have the mindset where they see whether they're invited out or not as a gauge of how much people like them. If someone doesn't invite them out they take it as a sign that the other person doesn't want to spend time with them. Like I said above, it's more a question of whether you're on someone's radar as a person they could potentially hang out with. Also, people tend to differ in how often they invite people to do things. Some are really friendly, organizer types. Others figure out what the rest of the group is doing and ask if they can come along (or it's just implied they can come). Others are more passive still. It's possible the other person could be waiting for you to invite them out.
Inviting people out and making plans is also a bit of a pain. You can't always leave the work in the other person's hands. Your friends shouldn't always have to be the ones to pick up the phone and think of something to do when they want to hang out with you. Ideally you each pull your own weight.
A final mistake is thinking that inviting someone to do something makes you look weak, desperate, or 'one down'. Don't worry about who invites who to do what and what it all means. If you want to get a circle of friends together assume you have to do all the work to make it happen.
They think they have to be super likable to have friends
Pretty much anyone can have friends if they want to. More often than you'd think you just have to be pleasant, non-annoying company: A buddy to shoot pool with, someone to play video games against, someone to go drinking with, someone to talk to about a common interest. Even an annoying person who makes an effort to be social and make plans with people will often have friends.
They actually aren't that interested in hanging around people
This isn't exactly a "mistake", but it can stymie someone's ability to establish relationships all the same. People who become lonely may be more shy and anxious in the first place or not have as much of a built-in need to be social. They may also have been ostracized in one form or another when they were growing up, leaving them a bit bitter and weary towards other people.
They may feel the painful effects of loneliness and isolation and want to escape them, but at the same time they're not 100% keen on being around other people. This can get them stuck in a pattern where sometimes they'll feel lonely enough that they make initial steps to get a social life going, but then they don't quite have the motivation to follow through on them.
They have a negative attitude towards people
Studies have shown that lonely people tend to be more cynical and negative about other people. This could be a cause or effect of being lonely, or both. In practice this manifests in a picky, superior, or snobby attitude. It may be an over compensation for insecurity, anxiety, or low self-esteem. It may also have roots in somewhat justified feelings of being different, left-out, and alienated. A past of social experiences that haven't gone well may also have left a lonely person feeling jaded about other people.