Playing classical guitar requires a combination of relaxation and effort/tension.
The right hand must be relaxed, period. A tightening right hand (and arm) is perhaps the most common fundamental error of guitar players of all types and levels.
The key to keeping a relaxed right hand is to start with a relaxed right hand.
To start with a relaxed right hand, we must start playing/practicing extremely slowly…and fully relaxed!
From there, we increase speed while maintaining accuracy…and stay relaxed!
To do this, we use a metronome. Strictly. Always!! We have a drummer friend that counts out time for us.
As we increase speed, we stay focused on accuracy…tone…and relaxation. We play until it feels natural and flowing and tension free.
When we stumble, we stop. When we stumble several times, we slow it back down.
In this way, we learn where our limits our.
Now, all the above is focused on the RIGHT (plucking) hand. The left hand is a very different matter.
The left hand is more like a ballet dancer, with a need to both both float and flirt lightly, but also to stomp and storm and really just about everything in between. This is because vast amounts of the tone production and hence emotive opportunity from striking notes on guitar strings is from the fretting hand, not the plucking hand! The left hand can do everything from completely deaden the tone and energy to milking it and making it sing.
Therefore, the left hand isn’t focused on relaxation. It’s focused on precision moves (adjustments) up and down the fretboard in a relaxed and controlled manner, and on hand/finger position shifts: literally, “fingers in this funny shape to fingers in that funny shape”. And then planting that shape and making it sing (or not) properly. There’s actually lots of “tension” in this process. So again, very different from the right hand.
This asymmetry in left and right hand physics on the classical guitar is a key reason for it’s great physical difficulty relative to many other (more symmetrical) instruments.
Please see the article on basic left hand warm up exercises for specifics around the broad relaxed right hand approach described above.