My puppy is 12 weeks old now and we've had her since she was 8 weeks. House training is going ok but only if the door is open and with the weather being so good it's been open most of the time - that's where the problem is, when the door is open she is quite happy to take herself out to do whatever but if the door is closed she just does it in the kitchen.  How do I get her to let us know when she wants to go out. 

Really, you can't just leave the door open and trust that the puppy will make the right decision without your help.  As you're seeing, the puppy might do that when the door is open - but because you're not rewarding it, you're not making it more likely to happen in future.  You're not really 'training' the puppy by providing a reward for the behaviour you like.  You're just leaving it to chance that what you want, happens.

You need to have a pot of treats by the door, and to take the puppy out frequently to the garden, rewarding the puppy immediately after having toileted.  You need to anticipate when the puppy needs to go and to take the puppy out even if she hasn't indicated that she needs to go.

Obviously when we first had her I took her outside regular, after meals etc and rewarded when she did anything so maybe Ive stopped rewarding too soon although if I'm with her when she does do it I do reward.

Shut the door - toilet training is too important to trust to luck and at only 12 weeks you've stopped too early.

Some dogs even into adulthood only ever give very subtle signs that they need to go out, so you are asking too much too soon.  You need to let her out at regular intervals, go with her, use a cue word as she wees, and give lots of praise (verbal, food treats, toys, and/or a play session).  Rewarding her when she displays desirable behaviour is the best way to teach her what you want and for her to learn what is required - you need to be right there next to her every time she wees or poohs so that you can mark that behaviour as one you like :) 

The good thing is that puppies are very regular in their needs - eat, play, sleep, toilet etc so it's quite easy to anticipate what to do and when.  Keep a diary if it helps but you soon know how long after eating she'll need before poohing (mine used to be 20 minutes ish at the same age) - weeing is usually pretty instant so I always take them out immediately after eating (actually I still do with the adults!).  Watch her like a hawk as you can be pretty sure she is signalling her intent to wee etc but you aren't reading it yet.  In particular take her out the minute she wakes up, that's always wee time, also she may start to mooch around the room, circle, look at her bottom or just develop a certain look prior to squatting...

The Puppy Primer by Patricia McConnell is a great book about puppy training in general, but it also has chapters on house training too and is an excellent book I would recommend.

>so maybe Ive stopped rewarding too soon

100% yes, definitely far too soon.  It is unrealistic to expect a pup to know that you don't want it to pee indoors.  They don't do it to upset us, they do it because they want to go.

As dogs don't have our thought processes, we need to show them what we want.  And frequently!  I always remind people that they don't expect their kids to know that you don't want a dirty nappy!

Keep up the attendance for poos and pees.  And this will mean even in the rain.  :-(  Throw a towel over your head.  :-)   And stay with pup until you get the desired poo or pee.  I have to admit that I am not in the least worried that my neighbours can hear me cheer and praise pup.  Puppies will respond to your excitement, and will know that they have done good!  :-)

I have a 15 week old puppy.  I expect accidents if I go out or don't open the door often enough.

None of my dogs ask to go out as such (well on occasion if they are desperate), I simply give them ample opportunity throughout the day.  Often like you the door will be left open weather permitting and providing they stay quiet.

I actually do not want my dogs to bark every time they want out training me to open the door for them throughout the day they would love.

In fact I deliberately ignore any attempt at barking to be let out and wait a minute before I offer them an opportunity, as there is nothing worse than a dog constantly asking to go out, come in, go out etc.

The last thing I want her to do is bark so I shall make sure I take her out regular again with treats and praise.  My last dog would just stand at the door if she wanted to go out at a time that was different to when she had been taken/let out. 

I have a bell that I taught my lot to ring by the back door[tried hanging bunch of cat bells on door handle,they chewed the cord, next got a cast iron bell and had that for a long time,could hear it all over the house] , started off with them playing with it but each time it rang regardless of weather I put them out, they soon learnt that they only rang when they really wanted out, wireless doorbells work great for this, just make sure the button is easily activated, I went and tried them out in B&Q.

To start with I rang the bell before taking them out, then got one of the dogs trained and the others learnt by watching her, any new arrivals will play with it initially but the novelty wears off when I insist they go out each time.

If your pup has had free access to outside then she hasn't learnt to hang on long enough to alert you and get taken out,she has to go right away.

Like Brainless, I never expect my dogs to tell me when they want to go out - if they do, it is a bonus.  I certainly wouldn't expect a puppy to do that.  I just provide them with enough toilet opportunities during the day to meet their needs.

I've found out little bits of apple go down well as a reward, carrots not to sure yet lol