You have to consider the geometry of your specific situation very carefully. Since you posted no pictures, and did not post a dimensioned plan of your situation, it is impossible to discuss your situation specifically.
Let me make a few assumptions, and give you some general ideas on how it might be done. This may not apply to your situation.
If you have joists overlapping above the load bearing wall (very common construction technique), it is likely that the ceiling of the room in question is attached to the joists. In this case, you can install the beam such that the bottom of the beam is flush with the bottom of the joists. This will require you to cut the joists back so that the ends of the cut joists are flush with the outside faces of the new beam. You would then install the joists using joist hangers, such as those made by Simpson.
This is a bit tricky to do in practice. You have to support the joists on either side of the new beam with temporary bracing adequate to hold up the floor. You also lose the joists as rafter ties during the process, so your walls could be subject to spreading loads with little to resist the loads. This may require temporary lateral load bracing during installation.
Once the temporary support is in, and the joists have been cut back, you install the beam on the columns, then proceed to install joists hangers, and install the joists. Once the joists are in place, you will have your lateral support back, and any temporary lateral and vertical supports can be removed.
Caution: the cuts to the joists need to be done carefully, if the joists are too long the beam will not fit, and if the joists are too short the joist hangers will not achieve rated strength. The temporary support must be bombproof, else you risk injury or death from collapse of the floor above.
Of course, your geometry may be different, and this approach may not work.
I have the need of this too.
Is it possible to notch the new beam and the joist half way? Kind of like a hybrid tongue and groove + dado joint is what I'm thinking. It seems to me the end result would be stronger, but there would be more work involved.
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