I'm a bit confused by your use of the term joist. Joists are the support pieces that go between (or over) beams, the latter of which are usually the large squared off logs, with joists being 2X material (usually 2X8 to 2X12, or in some of the older structures, lodge poles (6 to 8" in diameter).
If the sagging member is a joist, it may be as simple as putting a temporary joist up beside the old one, jacking it up with a screw type house jack (you will be lifting the sub floor and floor together), then replacing the old joist with its equivalent sized member. Make sure you have a solid base to jack from.
If the sagging member is a beam, this will be a little tougher, as all joists it supports will have sagged together and the normal 4" concrete floor is not strong enough to hold the jack(s). Unfortunately, its not as easy as jacking up the beam...there is simply too much to jack up at once....so you may have to individually jack up each sagging joist, prop them up one at a time, and keep doing this a little at a time until they all are up to the height you think is ok, then replace the beam.
A steel I-Beam could work, buy your local building code may not allow it in an all wood structure. The reason for this, is that in the event of a fire, the steel will lose structural integrity at about 3,000 degrees allowing the floor above it to collapse, whereas wood will hold up much longer to intense heat.