You can't.
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Some of them you get from quests, some from holiday events. And one you can only do if you are wearing a skillcape.
Talk to the dwarf near the entrance of the mining guild to retrieve your skillcape.
Firemaking, though it is very time consuming, it is officially the most cheapest skill cape there is available, only to Quest Cape ( Which isn't even classed as a skill cape ).
no you dont. to get a skillcape all you have to do is get your skill lvls like (wood cutting, mining and etc.) and get them to lvl 99. then you get an individual skill cape for each thing, like woodcutting. hope this helped. Wrong they are members only and you have to buy them for 99k which is a bit unfair though. And the skill dungeonearing can get up to 120 in lvl hope my answer helped.
Yes, sadly. Even if you obtain a lvl. 99 skill, unless you are a member, you cannot purchase a skillcape. Plus, they're 99,000 gp (or 99k) a piece. Talk about ridiculous!