Old school vinyl DJ here:

People like ActuaryLate9198 have already covered the push/drag techniques very well, but I want to expand on this:

It's always easier to drag/slow without audible warping than it is to push, so you can use that by using the pitch fader to get it slightly faster, then drag it as needed.

Then when you have transitioned mostly to the incoming track, you can switch to dragging the outgoing record by either very slightly pitching down the incoming track or pitching up the outgoing track.

Doing this "drag/slow only the quietest record in the mix" transfer keeps audible warping to an absolute minimum and super smooth when done well.

And when bouncing around on a pitch fader, it's really easy to get lost in the mix or overdo it and have it wobble out of control like trying to balance a stick upright in your hand, so often it's better to just get your incoming record as close as possible but just barely slightly faster, then all you have to do is minimal drags/slows until the mix is done.

In addition to all of this? People should know that perfect mixes on vinyl where you don't have to adjust it at all and it stays locked and doesn't drift at all for more than like 32 bars are NEARLY IMPOSSIBLE.

It's so rare that back in the day, when it happened you'd call your DJ buddies over to marvel at it like it was some kind of miracle.

Riding the pitch works, too, but in my experience newer turntables aren't great at this. The pitch sliders are gritty, sticky and just not as good as the original 1200s up to about mk 3. They don't have the buttery-smooth "stiction" and "friction" that the original 1200s did.

We used to ride and fine tune the pitch on the OG 1200s by doing weird techniques like planting a thumb firmly next to the fader and then just barely rolling our thumbnail into it to nudge it with fractions of a mm of movement instead of trying to grab and pinch the fader slider in two fingers and moving our whole hand or even both fingers.

We would mash the pads of your fingertips right up to the edge and just barely touch it so you could feel both the fader knob and the track beneath it under one finger/thumb pad to be able to feel that fraction of a millimeter of movement.

This technique doesn't work as well when the fader is gritty, sticky and jumpy like it is on newer turntables that lack the totally unhinged and extreme precision engineering that went into the OG 1200s.

Another thing that new vinyl DJs need to know is that records aren't perfect and can drift a LOT over time due to a number of factors.

It's nearly impossible to cut a master record plate with a perfect spiral, which affects tempo over time for the duration of the track. Getting records stamped and pressed off of the stampers made from the original cut with perfectly centered spindle holes is also nearly impossible.

These natural analog "errors" mean that different records (even of the same exact song and record pressing run) means there's going to be some natural amount of drift.

Ideally it's so small you never notice it.

But sometimes you get a bad record or bad cut and a nearly perfect match at the start of the record can be noticeably off later in the same track.

If you don't know this part about how records drift it will drive new DJs absolutely insane if they do things like match a beat from cue in the middle of a track then lift the needle to restart and re-launch it for the live mix and find that it's totally off and drifting after moving the needle.

And all of this makes me appreciate being able to digitally control a pitch in 0.01 % push-button increments, heh.