With timber or metal frame walls it is normally acceptable to support them on the existing floor joists (not the floor boards), either by providing a double floor joist underneath, if they run parallel, or across the existing joists if the floor joists run at 90° to the wall. (In both cases, there may be circumstances where additional support may be needed therefore it is strongly advisable to ask a structural engineer or surveyor to check the adequacy of the floor joists).
With masonry walls, which are heavier, the floor joists may need to be larger or, more likely, it may be necessary to provide a new beam. If the flooring is of a concrete construction it will be difficult to ascertain the thickness and strength of the floor therefore, unless it is certain, the lightest possible construction is advisable.
The support needed for a load bearing wall is likely to be more extensive, depending on the load the new wall will be supporting.
For a new wall in an upper storey of a typical house, providing support to the wall from the existing floor joists is unlikely to be adequate as the self-weight of the wall plus the load it supports will probably be more than the joists are capable of supporting. This may mean introducing a new beam, which itself should be adequately supported.
For a new wall at the ground storey of a typical house, the support needed will depend on the existing floor construction. If it is a timber floor then similar considerations for a new wall in an upper storey will be relevant (see above). Alternatively a new foundation can be provided beneath the floor, although the work in doing this may be difficult due to space constraints beneath the floor. A new foundation is also likely to be needed even if the floor is of concrete construction, unless the floor can be shown adequate to carry these new loads.
A new wall built off a new ground bearing foundation or slab should be provided with a damp proof course (DPC), at least 150mm above ground level. If the wall is formed through an existing concrete floor care should be taken to ensure continuity of the damp proofing by linking the damp proof course with any damp proof membrane in the existing floor. This is a difficult procedure to accomplish with damaging the membrane or floor.
If the new wall passes through an existing timber floor, the key thing to pay attention to is to ensuring that any new timber that is in contact with or supported by the new wall is above the line of the damp proof course. Also, if there is ventilation in the void under a suspended timber floor then air bricks in the wall are likely be needed to maintain air flow through the void.