My puppy sometimes asks to go out and when she is out there either digs up and chews the grass or the fencing around the play area. When she gets back inside she pees on the kitchen floor. There are 2 topics here really.
How do I stop her chewing grass and fencing.
How do I make sure she does her business instead of playing.

Keep her on the lead when you take her out to pee.
Then you can ensure she behaves as you would like in the garden, as well as knowing whether she peed or not.
After she has done her business, you will have the opportunity to praise her.

What a good idea thank you

Though we haven't had her much on a lead and i think she will probably think it is a play thing to jump up and catch!

I think you need to stay with her, most puppies will forget they need to toilet when let outside and it may take 20 mins or so before she does go. I would stay with her all the time,  (Give you the chance to distract her from chewing) keep repeting a word (we use Spend pennies) and then huge praise and a treat when she performs for you..
Then a bit more play and (Hopefully ) another wee then more praise and inside.
I have done this with all mine and now on a cold wet winters night I can open the door and tell them to "Go spend pennies" which they will in great haste then back in the warm and dry!!
Aileen

I do always stay with her but as I say though I know she needs to go she will someimes play. I say 'Hurry up' but I do that when she has been but she has started rushing to me for treats then and sometimes forgetting to go!

As I suspected. Not used to going on lead yet so just trying to catch hold of it and even less likely to get the job in question!

Ok, put a short lead on her while she is eating her food (hopefully she will be more interested in her dinner), and just leave it on for a bit until she gets bored of it, and just lets it trail behind her.
How old is she?
I used to keep mine on lead quite alot at toilet training stage even in the house, so i could spot when he needed to go to the toilet and then run for the backdoor with him. The lead was attached to my belt, so if i ran for the door he would come too!

We have been much better today but still she is playing with lead and not thinking about the job in hand but I am going to persevere.  At least she hasn't been chewing grass and fence! Thanks for other idea.

when she is actually piddling keep saying 'hurry up' in a nice jolly tone. and then praise when finished.
after a few days of that saying 'hurry up' will be a clear request to go pee to your pup.
Mines 6 months now and I do still have to keep an eye on her in garden to make sure she pees before playing as still young enough to forget why she was let out.

I think patience is the only key. She'll go when she really needs to as puppies can't hold themselves much anyway. Going to the toilet should be fun though, she has to enjoy doing it outside and if the whole experience includes a bit of play, then why not? As other people have said, repeat a command while she's piddling and she'll soon associate it with the actual action. As she grows older, she'll be able to do it 'on command' or at least understand what's expected of her. Right now, just be patient and encourage her.

When she does go I do say "Hurry up" - however I need to be careful as she may stop part way through knowing she is going to get a reward afterwards! I will persevere in this way becasue I know it will be good in the end. At the moment she just thinks going out on the lead is for play. When she gets bored of that - as I ingore her - she just sits down! I then try to get her up to do what she is supposed to be doing.