So I can't help with exact physics too much or exact electrical. Just a manufacturing engineer with too many hobbies.

At a basic level, you'll want to decide what you're making. While similar, the specifics will decide what you need exactly. A coilgun or mass driver uses electromagnetic coils in a series, 1 -> 2 -> 3 ect. Each coil is powered one after the other, with sufficient uptime and delay before the next to pull a ferrous carrier or projectile forward. Moments before it reaches the powered coil, that coil should shut down, moving the field further and continuing the acceleration. Note, as you accelerate the payload you will see a shorter uptime and delay at subsequent coils.

Of note: How you're moving the payload is important. If you're using a carrier, you will need to either account for its separation from the payload (consider a sabot in a shotgun shell, though many other designs likely exist) or its deceleration before the end of the line to avoid its self destructive impact. A carrier less payload needs some means of moving along with minimal friction, and must be ferrous so that the induced fields will interact with it. Most I've seen made used a non conductive tube polished smooth inside with each coil wound around the tube itself. Electronics on the outside, launching a steel ball bearing. Easily procured capacitors from cameras set up to each coil and confirmed to pop off in series. Either a LONG tube, or potentially hazardous electrical charges. Please consult a real electrician or engineer before using higher power inputs.

It's certainly been done quite often, but doing anything particularly impressive will be a bit of a feat without significant input.

A rail gun is actually far easier to make, if even less impressive without massive power inputs (potentially millions of amps to achieve the theoretical velocities a railgun is associated with) and precision manufacturing. Instead of creating a coil, a neat bit of physics is abused. Functionally, your design will resemble an elongated H, with the bottom legs extending as long as you'd like. Power source wires to the tops of each leg. The center portion serves to bridge the rails and complete the circuit and will also need to move up and down them freely. What this creates is a magnetic field between the center bridge and the power inputs on top. This field will propel the center down the rails. Every bit of rail behind the connection will generate a magnetic field as it does so. No need to time coils.

Sled is a must, as the center must contact the rails the whole time. The more magnetically reactive you can get the sled/payload, the easier acceleration becomes. Adding magnets to the sled isn't uncommon.

As with the coil gun, getting anything impressive becomes quite a feat. A demonstration of what's happening is fairly easy.

We've done childrens demonstrations as part of the company outreach like this. A magnet and paperclips will suffice. I would suggest a railgun and you start there, as the demonstration is easily found online and scale up from there. Uni project, not Naval bombardment being your goal.

I cannot stress enough. Please consult with someone knowledgeable in electronics if you start moving into higher power inputs. A demo model mishap with 9V is a tingle. Running 120V gets serious very quickly.