OK. first off, at the moment do you have a rose on the ceiling for the existing light? If you do, then it contains the connections for the lighting circuit, as detailed in the sticky post top of this forum. If you are happy to leave this in place, then you need to take a cable back up through the ceiling to each of the new lights in turn.
If you do not want to keep the rose, then you will have to lose it inside the ceiling void. This will involve making a hole in the ceiling, or lifting a board above it, to insert a junction box to do the same thing.
You have to get the connecting cable through the ceiling to the new light positions. This is relatively easy along the joists, but more tricky where you cross them. Again this may require lifting boards above to drill holes through centre of joists and thread cables.
What are these spotlights like? Do they mount into the ceiling, or on it? Do they have space inside for making connections to run the cable on to the next lamp, or will you have to use another junction box in the ceiling?