The first one is a love letter. For this you will need a white nail polish, a black nail art pen and a red nail art pen. To do this love letter design paint your nails an opaque white. Then use the black to create the lines shown in the picture. Finally draw on a small, red love heart. This is so easy and super cute.
I love this next one as it's not typically Valentine's themed as it doesn't have any red or pink but it still has a heart in it. For this you will need a navy blue polish and a white nail art pen. Once you have an opaque blue base, draw on the white heart with the pen and fill it in.