(Outfits from left to right)
1- Layer your tops. Less layers than in Winter. Add with a skater skirt (floral is pretty for Spring). Try cardigan in a pastel shade to cover arms.
2- Swap the Winter coat for a denim jacket.
Paired with a floral dress and belt makes a very sweet look perfect for days out. Add a thin scarf if it's windy.
3- Go from long jeans to shorts. A sweater and shorts is lovely together as it gets your legs used to the sunshine before the summer tan. A thin one is perfect for spring. Or you can wear a t-shirt and shorts when the sun is warm.
4- If it's not very warm skinny jeans look great. Pastel ones are fun in spring or floral printed ones but, paired with a pastel blouse suites the spring feel.
Pastels and florals shed the light on the very dark Winter and add an edge of variety into a wardrobe/closet to differ from winters thick and often covered up dark tones Winter fashion tends to be.
The transition is difficult. Think about mixing different prints (floral and lace) and lightening fabrics. For example go from a thick wooly winter scarf to a thin chiffon one. Or change a big coat to a denim jacket.