I suggest you put 3 things on her plate. Two that she is familiar with and 1 that she hasn't tried. Since she is 3 years old I would tell her that she gets 3 bites of all the different foods. (If you feel really guilty about this you can try starting with 1 bite of the new food). She has to eat her 3 bites before she gets more of the foods that she likes. This way you know she is at least getting a little food so she isn't starving until the next day, but you're encouraging her to try new things. Ideally, she can not get up from the table until she has tried the new food. Here is a warning, though, if she is very stubborn and you are going to feel guilty, I wouldn't try this, because if you tell her that she has to stay at the table until she tries it and then you give in when she cries, or stays at the table for a long time, then you will only be reinforcing the negative behavior.
If you prefer positive reinforcement you can try something like a sticker chart... She gets a sticker every time she tries a new food. After she gets 5 stickers she gets a small treat... This can be something small like a McDonald's toy, or it can be a special treat like going to the park with Daddy, special art project with Mommy, etc.