Letting a dog run on tennis courts wears down nails really well.
The other posts had some good suggestions about starting slow, I just have a couple things to add....
Here is what I do to train for trimming
1) Show your dog a treat and then hold it in your closed fist on the floor.
2) Wait...... your dog will probably sniff the treat, and eventually they will paw at your hand. The minute they do, open your hand and give them the treat and praise them lots.
3) Repeat a couple times, and over a few days. If you use a clicker it will usually go faster, but you don't have to.
4)Once she has the idea, and is offering her paw when you put your hand down, start turning your hand over and when she puts her paw in it, give her a treat from your other hand. Eventually you will have a pretty reliable 'shake' when you hold out your hand.
5) Get out your nail clippers and lay them to one side. Hold out your hand and once she gives you her paw, touch her foot a little bit and give her a treat. Let her sniff the clippers and give her a treat. When she offers her paw, touch the clippers to it and give her a treat.
6) After she has decided all the above is ok, try clipping a BACK FOOT nail and praise her like she just discovered the cure for cancer. Most dogs don't seem to be as sensitive to having their back feet touched.
Continue on in this vein maybe only doing one nail a day and always letting HER offer you her paw. If she feels like she has some control over the whole thing, she will be less frightened.
If she has a reliable 'leave it' you can put a pile of treats near you where she can see and dole them out. She will be motivated to let you do more if she can see the reward.
My dog also had paw issues when I adopted her. I used REALLY smelly yummy treats, and if she didn't offer her paw sometimes, I just told her to leave the treats and walked away. Eventually she would decide she wanted the treats more than she minded the nail trim, and would offer her paw.
I never give 'all done' treats. When I am done, I leave. All the good stuff happens while her paws are in my hands.
I keep the nail clippers in the kitchen and whenever I have a little piece of something yummy I clip a nail here and there.
I have found when starting out that it was easier for me to see where the quick was if I had my dog lay on the couch and I sat on the floor so I could see under her nail and be able to bring it close to my face w/o stretching her legs into uncomfortable positions.
Oh, and make sure you have really sharp clippers. I take mine to a knife sharpener who does them for like $3. If the clippers are dull they will crush the nail, not cut it.
Good Luck!