Hi there... I don't think there's an easy way to do this - you have to just talk to people and keep on till you find some like-minded soul, and, with luck, it'll burgeon from there... Of course, how easy it is to do this depends a lot on your character. I'm naturally quite reserved, so find it hard just to kind of march up to people and say 'Hi, I'm Tuo. Who are you?' but sometimes all you can do is grit your teeth and give it a go. If you're confident enough to do so, you could, however, try just coming clean and saying (perhaps to the vicar or someone who looks 'official'): 'I'm new and I don't know anyone, but I'd like to be more involved - can you introduce me to a few people?'.
Is there a coffee hour after the service that you can go to? Sometimes there will be people there specifically tasked to look out for 'newbies' and to introduce them to others. Or people may well talk anyway, especially (IME) if you have kids of a similar age. Are there kids that your children know from school? Could you take that as an opportunity to introduce yourself as 'Tuo Minor's mother' and start a conversation about school?
Can you volunteer to help with something - even if it's something quite low-key at first? I find that the weekly notices often take for granted that everyone knows everyone else and will say things like 'Mrs Sproggit is collecting knitting wool for homeless kittens; if you can provide any, please see her after the service'... which is fine, unless you don't know Mrs Sproggit from Adam! But you can use something like this to open a conversation on the lines of 'Hi, I'm new, and I don't know anyone, but I have some knitting wool at home that the kittens could have, could you point me in the direction of Mrs Sproggit?'. That way you start to feel more involved and also meet a couple of people and it's less 'exposed' somehow than the 'Hi, I'm Tuo' approach.
Finally, given that you want to find ways to explore and strengthen your own faith, could you talk to the vicar and ask what they have on that you might attend. S/he might be busy and/or in-demand (cornered by Mrs Sproggit and her tales of kitten-related woe, no doubt) after the service, so maybe phone or email some other time or make an appointment to see her/him.
Just a few ideas... I'm sure others will also have some. Good luck. It took me a while to stop feeling like a fish out of water, but I persevered and it was definitely worth it.