Over time you can expect your skills to improve through practice and all that good training provided by Computer. To represent this, at the end of turnsheets 3, 7 and 10 you gain an additional point to spend on skills only.
You may only spend this point on skills you have used in the turnsheets since your character was last upgraded. For example, if you have no skill points in Stealth, but have been attempting (and probably failing) to sneak past guards, you can buy basic stealth. If you have no Exploring but have spent time being led through winding tunnels by someone who does, you can probably justify your first rank in it. However, if you have expert Agriculture but haven't actually seen the inside of an algae pod in the past 6 months, you cannot take a specialism in algae breeding.
Quirks can only be gained (or lost) through appropriate roleplay. For example if you want to get cybernetic implants, discuss it with someone from the Department of Medicine — or someone in Blackout. If you're deliberately trying to gain a quirk please tell the GMs, we may misunderstand your intention otherwise.