Art Nouveau style is a particular form of art that is based in organic beauty as opposed to classical, academic art. Typical decorative elements include leaf and tendril motifs, intertwined organic forms, mostly curvaceous in shape, although right-angled designs were also prevalent in Scotland and in Austria. Art made in this style typically depicted lavish birds, flowers, insects, zoomorphs, and female images.

Style characteristics:

Simple base form
Flowing lines (often with stylized corners)
Organic motifs
Curves
Celtic design influence
Japanese influence
Female allegory images
Sculpture elements
Mythical creatures
Use of negative shapes (empty background areas)
Use of negative space (cut-outs)
Contrast of vertical rhythm and elaborate details

Check out this nice tutorial for a round coned shape:

Build a vessel in the Art Nouveau style. Select at leas 3-4 characteristics that you going to incorporate into the piece to make it fit the description of the style. Use a combination building technique. Sketch your piece and the construction steps you are going to take.

Build the base form:

step 1 - template

Start with a template - use a piece of drawing paper to create one. You need to do a very careful planning.

Base form can be round:

... or "boxy"

Plan your templates to achieve the desired base form: whether it's "boxy" or round.

step 2 - slab

Roll a piece of slab about 1 cm thick.

step 3 -shapes

	Trace the template on the slab. Use needle tool. Don't try to cut it right away - take your time.
	Cut the pieces by repeatedly tracing the shapes with the needle tool.
	Cut the sides of your shapes that you are going to join at 45 degrees for shapes like pictured here. For simple "box" type forms or round ones - you don't have to.
	Lay them out and get ready to attach them.

step 4 - putting together

	Score
	Shape (if needed) to prevent from cracking in future.
	Slip
	Join all shapes.
	Use coils for the corners.
	Smooth
	Make sure the joints are strong on the outside.

step 5 - adding details

	If you want to add a stand - make another template. You need to make sure all pieces will fit together.

	Cut "feet" if you need to
	Put everything together. Don't forget to score and slip when joining the pieces. Smooth all sides.

Decorating

step 3 - cutting and carving

	Use a needle tool to sketch out the design that you want to carve.
	Don't go too deep.
	Make sure the design flows from one side to another.

step 4 - attaching pieces

Roll thin slabs and cut out shapes that you want to attach to the base.

Don't forget the "score & slip" routine when attaching.

Decide if you need an extra support for the base - it can get really heavy.

Keep adding decorations.

Step 5 - finalizing

	Carve smaller details at this point.
	I like to use a wet soft brush to smooth everything and to get rid of "crumbs".
Don't forget to sign your piece or to add a signature stamp.