Most people who casually experiment with electromagnetic fields construct simple electromagnets using common household items. The most common way is to coil some copper wire into a solenoidal shape, which is like the shape of a metal spring, and connect the ends of the wire to the terminals of a battery or power supply. Once current starts running through the coiled wire, an electromagnetic field is generated. You can strengthen the electromagnetic field generated by such an apparatus in a few simple ways.
Increase the current running through the wire coils or solenoid. The stronger the current running through the wire, the stronger the magnetic field. You can increase the current by connecting the ends of your copper wire to a stronger, more powerful battery. Or if you are using a variable power supply, simply turn up the voltage dial.
Add an iron core to the wire coil. Instead of leaving the center of the solenoid empty, run an iron nail through it. An iron core through the solenoid can multiply the strength of the electromagnetic field by tens to hundreds of times.
Tighten the wire coils. The more times the wire coils in a given length of solenoid, the stronger the electromagnetic field will be. For instance, if your copper wire is coiled 100 times around a 2-inch iron nail, try to push the coils closer together and wrap the wire a few more times around the nail. If you can increase the number of coils to 150 coils on the 2-inch nail, you will increase the strength of the electromagnetic field proportionately.