I suppose if I remembered my calculus, I could remember how to construct an infinite series that would allow me to calculate pi to any desired degree of exactitude. But I don't remember enough to do that.
The most common method was memorizing a chunk of 15+ numbers each day, and adding it to the prevoious day. My favorites were the "poems" (some are available online, going as far as 740 places, others were actually made by my students). The trick is that the first word has 3 letter, then next has 1 letters, then 4 letters, then 1, then 5... "Did I pass a truck Wednesday?" gives 3.14159. Memorizing the poem seemed much easier for those who tried it. (Most of the boys were turned off by the idea of reading poetry, of course, LOL). The most creative I had was a the girl who went to 245 decimal places (tops for that class). She wrote a song (the tune was akin to a military cadence), but it contained several groups of explicit numbers, references to addresses, zip codes, area codes, musical groups, etc. I'm still not sure how some of her associations worked, but they worked for her, and that's all that's important.