I just start taking interest in the guitar a few days ago (as I need something to do during quarantine) I’m working with an old Daisy Rock guitar with a battery powered tuner, and have learned some of the basics from my dad. I would ask him if he wasn’t working and he had some more experience, but alas. I already know how to tune my guitar, and I always check that the pitch is just right by playing the strings from the one I start with to the one I tuned last., but every time I tune one string, the pitch jumps around making it really hard to the right sound. And once I think I have it and move onto the next string, then go back to check, the strings I just tuned are jumping around again! Could have something to do with the guitar being old or maybe needing new strings?
This really could be a number of things so might need some more info on the type of guitar, electric, acoustic, nylon or steel strings, does it have a whammy bar etc.
It could just be old strings, it could be the tuner is not very accurate, you might have more luck with the tuner if you can play harmonics at the twelfth fret but if you’re a beginner then that might be difficult for you to do. It could also be a damaged neck.
If the guitar is quite badly out of tune then it’s quite possibly normal what is happening. You have to keep refining until you get there. When strings are quite far out of tune then they need to be stretched or loosened, i.e., the tension increased or decreased. As you get one right and then move to the next one, the change of tension will pull on the neck, which in turn alters the tension on the strings you have already tuned. This will keep happening until all of the strings are almost where they should be, at which point the changes in neck tension become minimal.
Also, if the strings are new then they carry on stretching until they even out. The best way to overcome this is to over tighten them all slightly, maybe a semitone or two but obviously be careful not to snap them.
Could this possibly be your problem? If so, just keeping going through all six strings in turn repeatedly, eventually the neck tension will settle.