Putting together some of the parts of the other answers, and focusing very specifically on the OP's "current technology" requirements, we actually have a very limited tool-kit to work with.
Detection of deep space objects and threats is the first and foremost problem: until we know it's coming, we can't do anything about it. There are several groups observing for objects that are on Earth crossing orbits, the best first step would be tp place them under a singular organization th ensure continuous monitoring and identify and plug gaps in observational capability, either by deploying more resources or different ones (telescopes capable of observing in different wavelengths, deep space radars and so on). This might actually become one of the missions of the proposed US Space Force.
Once a target is identified, we need to find a way to deflect it. Since the odds are the object will be small, dark and moving very quickly, it may be detected with only a small window to react. in that case, using a nuclear weapon to heat and ablate a portion of the object to create a rocket like thrust to change orbits may be the only feasible defence. If we are thinking ahead, it is possible to build nuclear warheads that can concentrate much of their energy in a narrow direction, much like a convention HEAT warhead can focus the explosive energy of high explosives into a narrow jet. The project was conceived in the 1960's under the name CASABA Howitzer. Prebuilt warheads using these principles will be more efficient in focusing the energy of a nuclear explosion onto the target, so can be smaller and easier for a rocket to carry (or carry multiple warheads, if that is desired).
Finally, we will need a large and powerful rocket to carry the warhead(s) to the target. Currently the best option would be to contact SpaceX for a Falcon Heavy. This is currently the largest and most powerful rocket in service, giving us lots of options for interplanetary orbits for intercept, and also is the only rocket essentially built on an assembly line, so can be ordered and assembled quickly, assuming no one has a rocket already on standby somewhere.
So the order of events would be observe the target and calculate the orbital parameters. Prepare a contract with SpaceX to build and prepare a Falcon Heavy. The USAF or other nuclear force prepares one or more warheads on a missile bus to mate with the Falcon Heavy, and prepared the flight computers.
Once the assembly is put together, it is launched under Space Force control, which ensures the missile bus is guided to the rendezvous point, selects the optimum time and place to fire the warhead and releases it from the bus. After the explosion, observations take place, and if necessary secondary explosions are conducted to ensure the object is pushed far enough off course to miss the Earth. The missile bus will continue on its orbit, and if any warheads are not used on the mission, likely detonated to prevent their recovery sometime in the future.
So for the foreseeable future, this is what an asteroid deflection mission would look like.
Edit to add (just because!): the launch would sound like this.