On encountering the welcomer:
Do not, on a first encounter, fill in a sheet to be contacted. This can wait. If you have never encountered a church before, it can be distressing, in your first week, to be on the flower rota or to have to join the "Prayer Ministry Team", or put forward as a potential ordinand. Take your time, and keep your personal information personal.
Do say "thanks, I'm just looking around. My children's names are protected under the Geneva Convention. And my husband/wife/Civil Partner/ Significant Other will probably never attend Divine Worship as s/he is a militant atheist/allergic to incense/exploring Buddhism/fighting for ISIS/convinced that the Church of England is Babylon."
On being offered a prayer book and hymn book, just accept them. They may have spores, but it may well not be anthrax.
On being offered a prayer book, hymn book, notices and additional hymn sheet - demonstrate your juggling ability.
If you have children under the age of 16, there may be Sunday Club / Sunday School provision made for them. Make the most of it. You may be in charge in 3 weeks' time.
If your children are under the age of 6, and there is no Childrens work or you have wandered into an "all age service" that consists entirely of readings from Barth's Church Dogmatics, you may be told you will never be welcome again. If this happens, presume it is God's judgement on that congregation, and go find another one that still wants to exist in 20 years.
Do not mention you can play an instrument. Do not comment knowledgably about the Amin6 in the closing cadence. Do not do "air guitar" if there is any suggestion you understand pentatonic scales or have the vaguest idea what an Emaj is. Let people assume you know nothing about music. Then the worst that can happen is someone tries to recruit you for the choir.
On the other hand, instead of everyone being after your time and attention - there are some places where nobody will talk to you. Do what you like - hang around with a cup of coffee, inspect the stained glass, set fire to the vicar - you will just be assumed to be a stranger and left to it. Don't worry you're being ignore. Enjoy this. At some point in the next 40 years, something unrealistic and arduous will be expected of you.
When choosing a pew / seat - be aware that they are all "taken" - at least potentially. Arrive as late as you possible can - that way you can get a better idea of where is generally free.
Do sit as far back as you can. That means you will avoid the danger, if you are at the front, of standing up when all the "regulars" behind you are sitting, or kneeling when everyone else is doing the hokey-coley. Should this happen, everybody will tell you it was fine, and nobody noticed. Do not believe them - they saw it all, and they're all laughing at you. To repeat - arrive late, and sit near the back.
Communion services are quite odd. If you don't know what a "communion service" is, you need a more advanced guide. Basically, if someone you don't know suddenly walks up to you and offers to shake your hand - reciprocate. If the greasy bloke in the choir who's been watching you throughout the service tries to hug you - knee him in the canticles. If anyone tells you they believe in sharing a "holy kiss", tell them you're from Glasgow or Millwall.
Different churches have different rules on when people can receive Communion - either after they have been baptised, or when desirous to be confirmed, or after confirmation. Any given new church will have rules you can't anticipate. Best is to to go up when everyone else does (sitting at the back will help you judge this) with your hands crossed over your chest for "a blessing" - at least until you're made a bishop. Otherwise someone will think of some reason why you've been a bit premature in receiving.
Do not assume that the person who is really friendly to you before / after the service is just being friendly. They may be the person who has just done the "church welcoming" course, and will follow you round for days to come. If you are male and have given hints you are single/widowed/divorced, they may just be trying to get in quick before the rush. If they are wearing a dog collar, they may be the vicar. In which case it is his/her job to be friendly. If you live in a country area, and it is the vicar, don't worry. They'll be off to the next service in four minutes.
Most important of all - do not assume that the above is exaggeration. You may think I'm implying that people in Church are weird. This is because they are. The important thing to remember is - so is everyone else. Church people are no more weird than anyone else. They just have a sneaking suspicion they might be weird, and a vague hope that God can do something about it. They're probably right, but timescales are important. Remember that 1,000 ages in God's sight are the equivalent of one evening - what's the chances he's going to be doing a rush job?