You have already received a lot of good advice, but I want to tell you something truly different.
The people who mentioned that your daughter's fine motor skills are probably not ready for her to be writing are correct. You should work on activities to exercise those muscles. Play dough is an excellent "hand excerciser." Have her play with it a few times a week to strengthen hand muscles. Another option is shaving cream. It really works best on a table that is not white. Spray some shaving cream out in front of the both of you, spread it around, then show her how to use her finger to "write" in the cream allowing the table underneath to show through. You don't have to just do letters, you can also do basic shapes, numbers, even patterns (a bunch of vertical lines, then horizontal lines, etc.) If you can't deal with the shaving cream, put some colorful hair gel into a zip lock baggy, and you can get the same effect, just on a smaller scale. Coloring is also a very good idea, but don't just limit it to coloring books. Just get some white typing paper and let her do unstructured, freeform coloring and drawing. Yes, show her how to hold the pens, pencils, crayons correctly, but do allow for some creative changes like holding several crayons at a time for rainbows and using the side of a crayon for rubbings - the goal is to exercise those little fingers. A good motivator might be some really cool markers or pens - like glitter pens or gel pens. As for crayons and pencils, get the fat ones first, she may not be able to grasp the thin ones yet.
In addition to these fine motor activities and mock writing activities, read with her, a lot, everyday. Get some books that teach ABC's. My son likes those "I Spy" books - we have one for ABC's and one for 123's. Also get some of those ABC fridge magnets. The goal is to be able to identify each letter.
When she's a little more prepared for writing, search for "free handwriting worksheets" online. There are lots of resources out there.
My son's 3 year old class had a fantastic way to do some writing. The used a handwriting worksheet maker and printed sheets with the children's name on it. They made multiple copies and placed them in a three-prong folder. Add a pencil, and they called them their "journals." Each day during "journal writing time," the students were to get their journals and complete one sheet (tracing their name about three to four times). Not only did this focus on exercising those hand muscles, it also taught the kids to recognize and spells their names!!!