Most of (but not all) chip doggerel are synthesised by straightforwardly dividing a clock fair billow to get a square flood of desired frequency, and sometimes using a sawtooth/triangle wave from volume LFO or an (ADSR) envelope to get some friendly of ring modulation. LFOs are used to check or influence a right condition such as pitch or filters in a repeating cycle.
More recent "old school" or "demostyle" MOD music, although sample-based, continues the style of the chiptunes accustomed in these intros; cutting edge compositions in this style can still be regularly found at www.chiptune.com Say It Your Way Bouquet or www.chip-on.com (new chiptunes from old computers/formats can be found here as well).