There are at least two parts to this (possibly more) -- the parts that I can articulate are these: 1) recognizing that fears are not reality, and not allowing them to attach and 2) squashing doubt with evidence. 2 is harder because it involves unlearning, but both are the same process. With 1, you feel your emotion, but you compare it to your set of knowledge and see that it does not make sense, and you acknowledge that it is not true. For instance, if some offhand comment by a lover made me worry that they did not want my company, I would consider how often they invite me to spend time with them, how happy they are to see me, how often they reach out to me, and if those things were all high level I would understand that the comment did not mean what it sounded like and dismiss it. If this was a 2 situation, I would have a previously-formed belief that people do not want my company, which would make it much harder to dismiss. If I did have that belief, I would acknowledge it to myself and realize that it would bias my views. Then, most importantly, I would keep a mental list of all the positive things that showed a desire for my company, and run over those again and again in my head, over and over, remembering and remembering -- OFTEN, not just in crisis -- until the time I spent thinking and experiencing that desire for my company outweighed the time I'd spent experiencing/thinking about how people did not want my company. 2 is a loooong process, and I do not think it can happen without deliberately changing thought patterns.
Other people can help you with these things, reminding you of positive things about yourself or love or whatever, but for one that only works if you're trying to build faith yourself, and for another, it's hard work for that person, especially if you don't practice on your own and therefore never get better at it. If you rely solely on their reminders, you're going to wear them out; it's too big a self-project to be all external.
The thing is, most people employ these tactics already, very effectively, but in the opposite direction. They build their doubt in love or self-worth or whatever by reflecting only on the negative, over and over, and dismissing anything that would be evidence for good. I'm not saying don't talk about things that are negative: hell yes talk about them. Hell yes process them. This faith-building I am talking about is internal, self-talk: the thoughts you often don't even realize you're having, unless you watch for them.
And it's fucking hard when you don't think you deserve love, admiration, appreciation. That was the first thing I built faith in and maybe the most important. And part of it I built with a logic train based on faith: if love is necessary food for living beings (which I believe), every living thing deserves it. From there I practiced receiving love. It is very easy to block out love: it's kind of rare to be able to just accept it as your right as a living being. It takes faith to accept that when someone tells you you are amazing, it is because they are right. I don't really know how to articulate how I got from automatic rejection to acceptance because it was a leap. I decided to believe people's sincerity without edits when they showed me appreciation (instead of mentally appending things like "but you don't ask for my time" or "but you don't know how much I stink at this important thing"), and to stop using people's dislike/etc as a stick to beat myself with. And it took lots of practice and lots of mental backtracking -- responding to my habitual mental doubt-statements with faith-statements.
Also, if you're in problematic relationships, this exercise may make you realize the problems in it. If, with my previous example, my lover did not invite me to spend time with them, seem excited to see me, or reach out to communicate with me, that would not be evidence for the idea that they did want to spend time with me. BUT it would not necessarily mean that they did NOT want to, either! I would need to discuss these things with my lover and find out what was the cause of these things. Concluding that they were evidence of my unwantedness would be a massive assumption (one which I have made before and try hard not to make now!), and one that would be VERY hard to disbelieve later. It's much harder to unlearn a belief than to simply not adopt it. When considering the evidence does not result in increased faith, that means that it is time for a talk to increase understanding, or possibly to renegotiate the way the relationship works.
I've been reflecting a lot on this lately and feel I have more to say, but this is long enough.