I have a question. I am planing to write to a fairy-tale like a Brother Grimm or Hans Christian Anderson type of fairy-tale set in the modern time but after conducting research(reading fairy-tales of these literary greats). Its hard. I know every story is so different and so unique and that's whats make them awesome. The delima is that i need to know what are the typical features of a fairy tale especially a princess and prince story. These kind of show how girls should follow their dreams etc but i can't really understand how i should establish a plot. What should be the climax etc. I hope you can help me.
You are confusing a traditional fairy tale with the Disney version of it.
The traditonal fairy tale does not "show how girls should follow their dreams". They either show how disregarding common contemporary moral standards leads to a tragic end, or how acting in accordance with morality leads to a happy end.
Cinderella does not get the prince because she follows her dreams at all, but because she works hard and diligently, is honest and kind, even to her stepmother and step sisters who treat her bad. Her sisters on the other hand follow their dreams of wealth and marrying the prince and are punished for their greed and unkindness! Cinderella does not aim for nobility and riches at all, she is rewarded with true love because she is a "good" person.
The little mermaid in Anderson's tale dies, because she follows her dream! Snow White gets the prince because she diligently worked as a servant for the dwarves. She did not even know that there was a prince, she never aspired to anything beyond her current lot. If anything she was happy as the maid to the dwarves! And so on. Fairy tale protagonists don't succeed in pursuing their dreams. The fairy tale morality is quite opposed to current American individualism. Fairy tales reward subservience, modesty, humility, loving your parents (even if they are evil) and so on. And fairy tales harshly punish stupidity! Think of all the nice persons that get killed just for being naive.
Fairy tales tell you to:
What you are looking for is not the structure of the fairy tale, but the common Hollywood romance plot.
As I mentioned in my comment above, the Aarne-Thompson classification, specifically the section on fairy-tales, may be useful to you. A handy summary can be found on Wikipedia. It classifies stories by theme and gives common examples which are likely to be familiar to you. It also lists lots of fairy-tales that have become forgotten in recent years, which you may find inspiring to your story.
Fairy stories are classified by the role of the suprnatural in the plot. If you want a "prince and princess" story you might look at stories with supernatural wives or husbands, of which there are many: East of the Sun, West of the Moon is a semi-well-known example. The Frog Prince might be more famous. If you do take to this plot, absolutely check out the tale of Eros and Psyche from Greek mythology, which some folklorists call "the first fairy tale".
If you want to learn about plotting fairy-tale stories I recommend you to read "Morphology of the Folktale" by Vladimir Propp. It is a study that dissect the different elements of the folk tales from examples and present a common structure composed by 31 "functions". It is easy to structure your tale after that schema. You can have a bit of it by reading Wikipedia article on Propp (Propp). However, if you are interested in the field like I am I recommend you to get your hands in the book. I recommend also to have a look at John Campbell's take on the monomyth (Monomyth) if you plan to write a heroe/heroine based tale. This one is more focused on the inner development of the hero than Propp's work.
I agree with another answer in that you don't seem to want the real traditional folk tales (i.e. gory original Grimm Bros. stories) but the decaf post-victorian Disney like version of them but that is compatible with the works I referenced.
Oh, it's easy! What you need is a villain!
First, think up a reason, why someone wouldn't want the princess to meet the prince. What is it in that connection, that someone might hate? Any reason?
Knowing the reason, think of means of keeping the two apart. Lies? Betrayal? Poisonous, controlling relationship? Dependence? Guilt trip? Force? Dark magic?
Then build the character around the motive and the means - flesh out the villain, and the relationship of that villain with the prince and the princess. Lurking in shadows? Pretending to be a best friend? Looming as an overlord? Being a competitive, jealous scoundrel?
Then, once you have the villain and his(her) power developed - you fleshed out the way of keeping the lovers apart in detail - start poking at it, looking for weak spots. Negligence, ignorance, paranoia, whatever vice the villain has that can be exploited to break through the barrier.
Then flesh out the royal pair, sharing between them skills and powers that will make overcoming the barrier possible, though difficult.
And then just write it down in order. Introduction of the actors, building their relationships, then fight against the barrier, breaking through the barrier, happy ending.
That's the basic structure, which you may convolute some, for extra effect. Like: The princess and the prince don't go along with each other in the least, and only through common trials they overcome the differences. Or: The meddler opposes the breaking through the wall. Another approach must be taken. Or: The meddler poisons the relationship. Or any of countless mutations, like the princess choosing not to marry the prince, or the prince appearing to be the actual meddler, with the obvious one being actually a "hard love" good person, or one of the lovers getting corrupted in the process... sky is the limit, but that's all just mutations of the simple scheme described above.
Fall in love with one another, hate each other at first, get lied about, always have misunderstandings, almost die, are betrothed to each other or someone else, involve a witch, have an evil/good stepmother, princesses are either helpless or more macho than the man hero, they try to quit being royal and go gallivanting off with peasants, always wonder why the bad guy is doing this to them, the first kiss is true love's kiss, have a death in the family, the sidekick who dies or is a bad comedian, and the list is sure a long one. See a couple of movies or books and you'll find more.
Establishing a plot: Sometimes you only have a few scenes to start with for your character to perform. Write them out, the story can/will grow from there. You're in control of who and what your story revolves around. What do you want to happen?
Climax: Depends on what you find out about your character and what's in and what's going on in their world as you write about them.