When you learn to write, it feels hard but that's just because you haven't got used to the movements yet. As you keep moving, bit by bit, you get more accustomed; that's what it takes to build strength.
Tips for building strength
You shouldn't have to use too much strength to press a string down. However, especially with steel strings and chords, fretting can be a tiring business. Some fingers might also be weaker than others, but they all get stronger with practice.
You can strengthen individual fingers and wrist muscles by squeezing a clothespin, or the whole hand by squeezing a tennis ball.
Tips on improving your coordination
If you're not used to fine motor tasks, it might be hard to get your fingers to obey at first. Try these exercises to develop your finger control:
- Place your hands (especially your fretting hand) on the desk, and lift your fingers one at a time.
- Think about the number for the finger you're lifting (1 for index, 2 for middle, 3 for ring, 4 for pinkie) or say it out loud.
- First lift them in order from 1 to 4 and back, then start making different patterns, like 1-3-2-4, 4-2-3-1.
- Try not to look at your fingers when doing it.
You can also place your other arm in front of you and then grip it like it was a guitar neck. This way the hand orientation is the same as when playing.
Make a habit of exercising your fingers, e.g. in traffic jams, at school/work, when watching TV... but concentrate on your fingers.