Two year olds are great for testing your patience (althougth I personally think that 3 is much worse). It's totally normal for them to tell you "no" at this age. Here's how I would handle it:
To stop the whining, tell her that you don't listen to whining and if she wants something, she needs to ask in a nice, big girl voice. If she whines, ignore her-act like you don't even hear her. If she throws a fit, remind her that you don't listen to whining, etc. In the meantime, whenever she does use a normal tone, praise her for it. This usually does the trick.

In regards to her telling you "no", keep your cool, and say something like "You will not tell me no" and then physically direct her towards what you wanted her to do (so if you asked her to pick up a toy and she tells you "no", take her by the shoulders or the hand and walk her over to the toy you asked her to pick up). This does 2 things-it lets her know that she cannot tell you "no", that it's disrespectful, and also gets the point across that she can say "no" all day long, but it isn't going to phase you because you're going to make her do what you asked anyway. Essentially, the word "no" loses its effectiveness for them.
Be very consistent, and I'm willing to bet these things stop pretty quickly.

Hope this helps!!!!

Pixie nailed it. My 2-year-od behaves exactly the same way. Now that she is approaching 3, it's getting a little better (bedtime battles getting worse). I can't say anything more than #1 (she gave me great advice too), except that you are not alone, your kid is not an alien, and (somewhat) better times await you.

It could be worse. Our neighbors around the corner have a daughter the same age as mine, and they just came home with twins.

Ignore it, and teach her another way. My daughter did the same, cause my husband is a pushover with her. When he left for two months, every time she whined, I would explain that she can't talk that way, I don't understand, yada, yada, but she needs to say what she wants nicely, and she'll get it. If you don't want to give it to her, then explain, don't give her that, and ignore the whining. It worked great for me. It was my husband who was reinforcing the whining, I was going crazy from it. As for 'NO's, ignore. It's good that she knows how to express herself. Sometimes I just wait 2-5s, and she turns around and does it anyway. She just wanted to say NO for the sake of it. When she really means it, I sometimes have to physically move her to where she needs to do what she needs to do, but I don't scald her for saying NO, she was just expressing herself.

1,2,3 magic by dr. phelan

read it.
study it.
do it.

it works.

its really so much more than just counting, which we have all seen, and has no real effect.

this is a very simple program, the book is cheap, but its priceless. it has changed my life!

in addition to using a method like this, be sure that she is armed with the skills she needs to effectively communicate in another way. If her verbal skills are limited by her age, teach her signs for things. Teaching them how to communicate with sign language is a great way to empower them when their verbal skills are so challenged, and really helps avert those so called terrible twos.

oh yes, i forgot to say...

never EVER EVER let the whining work.

If it works, it will continue.

and it will not only continue, it will escalate!

anything whined for is an automatic no... until the whining ends.

My daughter does the exact same thing. Though, I can thankfully say it is getting much better. She is beginning to not whine as much and use words when she doesn't like something. Their vocabulary is limited so I've told her if there is something she doesn't like all she needs to say is "No thank you". I tell her to use the same response rather than just shouting NO all the time. The only time I find "No thank you" unacceptable is when I've asked her to do something and she is refusing. I agree with DixiePixie. Make sure they know they aren't going to get away with saying NO.

Her vocabulary has really expanded though which makes such a big difference. We have to remember how frustrating it must be for them not being able to communicate what they want.

Signing is a great idea and works if you are consistent. Another thing I do if I sense that my daughter is becoming frustrated because I can't understand what she's telling me is I tell her to show me what she wants. She knows how to do that and I usually figure out what it is. Hope this is helpful and best of luck.

Thank you everyone for the advice. You sound like a pro DixiePixie. Lets see if it works for me.

wow it so nice to hear that a parent out there is going through the samething I'am going through. My daughter will be 2 in June boy does she wine all the time. She has always been a cryer and winer. it can be tiring. She want's me to hold here all the time she will follow me aroung the house wining and crying wont stop sell I pick her up or hug give some kind of attention. Even then does not last long. When she get's real bad I put her in timeout in her room. make her sit on her bed. She does stay on bed too. As I put her in her room I say" what u are doing is not nice" not good to say you are not good. Kids are what they do at times is not good. Every time she gets whiny i put her in her room I worn her first if she does not stop in the room she goes tell her when you can start acting nicer you can come out. Most of the time it works. If she says no to dad or something she should not do I tell her go say sorryand give kiss and hug. I tell both her and brother that. Works well. hope this helps. Nice to get so help.