Hey,
Here are some basic things to try:
Use two VCOs, or a module with two or more voices (Castor & Pollux or Doepfer's Quad VCO have this ability), and detune them from each other slightly to create a larger chorus sound. Patch each one to one separate side of a stereo output. Pan one just 3/4 left and the other 3/4 right. You really don't want to go hard left and right...you still need a little of each channel's audio to fill in the center. That makes for a much larger sound. Next, try the same thing with a single VCO, splitting the VCO output with a stacker cable or a mult and run the outputs to left and right that way. You may get some unexpected phasing results. Try it and listen!
Use one VCO to modulate another. Choose one VCO as your "primary" and a second as your modulator. Patch the output of any wave shape of the modulator VCO into any CV input on your primary (try V/Oct first, and then experiment with other inputs like FM, PWM or Sync, etc.). Now, adjust the frequency control of your modulator VCO to get some good FM sounds. This is pretty much the same as using an LFO, except that your modulation source is in the audio range. If you use a square wave or pulse wave, you'll get some interesting pinging effects. Route the pings through a bucket brigade or tape delay and adjust the timing and feedback levels to achieve some fun polyrhythms!
Using an LFO is a very basic function. Just like in #2 above, patch the output of an LFO into your VCO. Another cool trick is splitting the signal of an LFO and running half into your VCO and other other half into an inverter or attenuverter like Maths or Mutable Instruments Blinds. Then patch the attenuverter output back into the VCO and play with the modulation rate on Maths to see if you can get the VCO's output to "chase" itself. If you find the sweet spot, the VCO can almost ring itself at the crossover point (depends on the VCO's Q values, usually set by the electronic components). You need Math's movement for this to really work well.
If you want less drone and to control it with a keyboard, then patch in an envelope so you can use your keyboard (or beat pads or a sequencer or whatever) to control pitch and gating. If you do it this way, be sure to also run a cable from your gate control to the reset input on your LFO so that each gate opening starts the LFO cycle from the beginning (better control of the output sound).
Those things should get you off and experimenting with other ways to use oscillators as modulators! Try this with filters, too. Anything that outputs a voltage can be used as a modulator. The limits are up to your imagination! I always find that just plugging something into something else is a great way to learn more about modular.
I don't think one needs to dive deep into a single module to be able to understand modular. One does, however, need to understand the important parts of a "voice" (VCO --> VCF --> (EG) --> VCA --> OUTPUT) so that you can then know where to adjust and insert and modulate. I recommend working on building a voice first, using whatever modules you have, and then start adjusting and plying just by inserting movement CV (Maths, any clocks, LFOs, other VCOs) into your patch to see what changes are made.
Have fun! Keep asking questions!
"I'll just plug this in here and see what happens."