Identify the load-bearing beam or structural beam to be removed. Hire a structural engineer to examine it first to determine if removal is possible and can be done safely without bringing down the structure. Have the engineer detail the types of supports needed and where to temporarily support the area where the beam is removed.
Tape up and attach plastic walls to separate the work area from non-work zones to capture the dust from the repair.
Open the surrounding drywall with a crowbar and hammer to expose any wiring or plumbing in the adjacent area. Remove this material have turning off the wiring and rerouting the plumbing. Use a plumber if needed or an electrician's services.
Install the supports with wood and timber as the engineer pointed out, in exactly the locations identified. Make sure the supports are installed snug so there is no movement in them when stacked. Build the supports with nails, brackets and a hammer. Use multiple timber supports for added safety.
Remove all the drywall around and on the supporting beam. Expose the structural piece to its core timber or masonry. Begin removing the original beam as necessary using a saw, hammer and crowbar. Remove the entire section and clean it out thoroughly with a broom and vacuum.
Monitor the supports to make sure the weight of the structure is resting properly on the supports you've built for it. Continue your construction work as needed.