How can you produce different electric wave forms for experiments

What kind of device do you need to produce a variety of electric wave forms for different experiments, such as a rectangular biphasic square wave, a sinewave, or a sawtooth wave?

This is usually called a function generator. It provides a choice of waveforms and an adjustable output voltage and frequency and DC offset. Typical waveforms are sine, square, triangle. Some allow the rectangular waveform with adjustable duty cycles, and I think you might mean bipolar rather than biphasic (biphasic is a medical term as far as I know). Some have 'arbitrary waveforms' too. A file or table programs the voltage at different times, so e.g. a waveform like an electrocardiograph can be produced.. Also this could help with biphasic if your version of this is different from the available bipolar waveform. These are pre-recorded waveforms. Sometimes it makes sense to build up a simple circuit to produce some specialised waveform.

In some cases you may be able to use the sound card of a PC as a function generator within its limitations.

The link below shows mono and biphasic waveforms, which to a function generator are just bipolar or an offset bipolar so it becomes monopolar.

The most common device used as the basis for a waveform generator of hobby class is the 555 timer.

An Oscilloscope usually.