Give the vertices of your object a color (RGBA) with RGB white (to show a normal texture) and A (=alpha) a value for the transparency of that vertex.
Code:
D3DColorMake(R, G, B, A) 'with each ranging from 0 to 1
'or
D3DColorRGBA(R, G, B, A) 'with each ranging from 0 to 255
'and don't forget to turn alpha blending on
objD3DDevice.SetRenderState D3DRS_SRCBLEND, D3DBLEND_SRCALPHA
objD3DDevice.SetRenderState D3DRS_DESTBLEND, D3DBLEND_INVSRCALPHA
objD3DDevice.SetRenderState D3DRS_ALPHABLENDENABLE, True