There are six main tone holes on every woodwind instrument. In general.
Left hand on top (the top three tone holes with index, middle, ring), right hand on bottom (index, middle, ring again).
There's how to breath, how to put the reed on, posture, etc. too.
Maybe someone else who knows clarinet better will reply.
Tonguing too, embouchure....
Open is middle G. It's a Bb clarinet though (I'm assuming), so it will sound a whole tone higher than it reads.
left hand thumb covers the tone hole in the back. It should be positioned so it can operate the other key too though.
thumb = F
then index, middle, ring.... E, D, C. And that's what they read as middle C.
Adding keys each time. Then add RH middle for B natural. It breaks the pattern. Index RH would be Bb. Then 1 and 2 on RH, that's A. Then, 123 on TH, that's G. Low G. So thumb, LH123, RH123 is low G.
Hand position is important too. Curved fingers. Reed choice and placements on the mouthpiece.
Start with putting your hand over the six main tone holes though. RH thumb goes under the thumb rest and can hold some of the weight of the isntrument. They have little neck straps for clarinets now too. The weight can really make your RH thumb sore. The fingers also hold the instrument a little, but if it's a G, there's not much holding the instrument, just RH thumb and your mouth.
A above second line G is the little nub key over the the LH index. You should be able to tilt your LH index finger to hit that. They's why you need curved fingers. Put your LH three inner fingers perpendicular to the clarinet. Then tilt the second joint of your LH index finger toward the instrument, and the thick thumb muscle base part of your hand toward the body of the clarinet. That can get that curve thing going.
On the fingering chart, they probably show the complete set of possible keys and holes. The dark ones are the ones with fingers down. You have to use other parts of the hand, like the RH part where the index finger connects to the hand, for some of the notes.
There's more to it, but that's the basic idea. By the LH thumb, if you press that key down and close the thumb hole, it will send the pitch up a P12. Saxes are nice -- It's an octave key. Clarinets have a register key though. So that low G becomes four line D. That jumps over the register. Going from few fingers down, like up by G, A, Bb on the upper joint, to many fingers, like the LH/RH123123 and thumb plus register -- That's called crossing the break. It can be a challenge.
You play piano. You could trade some lessons with a clarinet player. Get someone to demonstrate in person.