What is the correct way to shuffle?
The best way to shuffle a deck is to use multiple different methods of shuffling one after another. As the rules state pile shuffling can't be used except at the start of the game that is perhaps the best way to start your shuffle. After that the Overhand Shuffle, sliding a few cards at a time from one hand to the other so that the cards in each group stay in the same order but the group order is changed, effectively several small cuts. A Riffle Shuffle, taking two halves of the deck, bending them in the middle and letting them fall a card or two at a time onto eachother, does the best for reordering the deck, but since it involves bending the cards it also does damage to them over time, some people won't use this method because of it, and it should never be done to another person's cards for that reason. A similar effect to a riffle shuffle is the Weave or Faro Shuffle (not to be confused with mana weaving), where two halves of the deck are held with a little space between the edges of the cards for the other half's cards to slide into, this is easier with sleeves because the sleeves will create that space between the edges of the sleeves themselves. Washing the cards also does a pretty good job of randomizing, though it looks ridiculous and takes time to spread all the cards out face down and move them around randomly with your hands.

It's all a balance of the level of damage you're willing to accept to your cards, and the level of randomness needed. I will riffle my pauper deck but not my $1000+ EDH.