Welcome.  I'm a newbie also.  Do you have a teacher?  There is a lot that can be learned from YouTube videos and the like but, at this stage, there is no substitute for the feedback from a teacher who will get you started with the correct fundamentals.  Even having intermittent lessons when you and a teacher are both available is worthwhile.  A teacher will get you over those obstacles in much less time.  

If you push it in and it still slips then the peg-to-hole taper may need to be matched or you may need to apply a little peg compound.

@Charles I am coming back to violin just the last couple of months, and working with a violin that is over 100 years old and with a E peg that my grandfather whittled, probably because it was sticking. Only took me a week to consistently and fairly quickly tune my violin using Fiddlerman's violin tuning app. I feel that the fact that I was breaking in new FM strings, probably affected the time it took. It is not that hard to nail the correct tone and lock it in with traditional pegs. Like previously mentioned, start just under the correct tone, move it up and push it in when you hit the right tone. Only peg that occasionally doesn't cooperate is the E string, but it is my grandfather's fault for whittling the peg. I suppose someone who has trouble telling when two tones are the same or different may have trouble, but the Fiddlerman tuning app actually uses tones of actual bowed violin strings which really makes it much easier for people who haven't got trained ears. Not sure about people that are tone deaf, but never met a tone deaf musician. I do have to admit that I have an excellent ear and can hear errors in recordings and live performances. I can also tell when a turntable drags and speeds up even if it is a minor fluctuation. Maybe I shouldn't expect the average ear to nail stuff as fast as I do. I have people tell me that, it means I have perfect pitch, but to have perfect pitch you need to know the notes you're hearing. I am just relearning sheet music and am retraining my ear, so far from it! I am pretty sure though, that Fiddlerman has it!

@ Charles @ coordinated? Me? HaaHa... You wouldn't say that if you saw me the first couple of days! I busted my new E string 4 days after I got my violin set up. Bought FM strings to replace the D'Addario strings, switched the A and E pegs (the whittled peg was in the A slot). Once I switched the pegs and carefully strung the FM strings. I started working on tuning. I had plenty of trouble with slipping, especially the first couple of days, but it got easier very quickly. I am basically considered a bull in a China shop since I have nerve damage and loss of feeling in my left hand fingers, and I am left handed! Keep in mind, I played violin for 2-3 years when I was 11-13 years old (in my late 60's now) and played in the school orchestra so I tuned violin with traditional pegs a lot back then. Yes, I am relearning but some parts are like riding a bicycle, and it is possible tuning, for me, may be one of those parts. Not sounding like a dying cat is one of the parts for me too. (I remember it from my first lessons). I do remember how to to get a clear note out of a string. I also, give more credit to my ear than my coordination, and a lot of credit to FM's awesome tuning app for being so easy to use and being the actual sound of bowed open violin strings.