The dictionaries translate these three words roughly as preparation/preparedness or ready/readiness.
I don't think I understand the subtleties of their usage. Not to mention できる also has another meaning, "to be ready", as in 「ご飯できてるよ！」to mean that "The meal is ready."
Please enlighten me. Also, are there any other words commonly used to mean prepare/ready?
Between 準備 and 用意, they're both used for preparing in advance, but 用意 puts emphasis on preparing things in advance so they can be used when the time comes, so is used more when e.g. baking a cake in advance, and 準備 is used in a more general way, like preparations for an athletics carnival or something.
準備 is also used in the expression 心の準備はできている, which is used for mental preparedness in a similar way that 覚悟ができている is.
覚悟 is used when bracing oneself for something which is going to be unpleasant, or preparing for something that will be dangerous/difficult etc.
支度 is particularly used in reference to meals e.g. preparing dinner (夕飯の支度をする), and preparing for the execution of something that's planned/done as a matter of course e.g. preparing for a trip (旅行の支度をする) or preparing for school (学校へ行く支度をする).
I believe 夕飯の用意をする is also used, so I think there's a bit of overlap.
備える is used for preparing for a disaster etc, or for preparing furniture or electrical appliances and whatnot so they can be used whenever they need to be.
できている can often mean something is in a prepared state ("ready", "completed" or "done" etc), and Xでできている means that something is made of X.
As far as I understand them, 準備 seems like doing something concrete as preparation to do something, or preparing for something to happen.
覚悟 is more of a mental readiness for something (心に用意のあること). The best way I remember this is that in the Street Fighter games, Chun Li often says this in her pre-fight intro (覚悟はいい？ ー Are you ready?).
用意 seems to overlap the two, but more with 準備 than 覚悟.
Another word to consider is [支度]{し・たく}. I've never heard of it before now, but apparently it is mainly used only in speech, and often just relating to food/clothing.
[用法]準備・用意――「食事の準備（用意）が整った」「外出の準備（用意）をする」「研究発表の準備（用意）をする」など、前もって整える意では、相通じて用いられる。◇「準備」は、「大会の準備をする」といえば、必要な物をそろえるだけでなく、そのための組織を運営することをも含み、総合的であるといえる。◇「用意」は「大地震にそなえて十分な用意をする」「当日は上履を御用意ください」のように、必要なものを前もってそろえておくことに意味の重点がある。◇類似の語「支度」は、必要な物をそろえる具体的な行動をする意に用い、「支度金」は必要品を買いととのえる金銭であり、「食事の支度をする」は、材料をそろえて調理することである。
Translation (I broke it up so it would be easier to read)
[Usage] 準備・用意 - In the examples meaning to prepare in advance,「食事の準備（用意）が整った]、「外出の準備（用意）をする」、「研究発表の準備（用意）をする」, etc. both can be used.
◇「準備」in sentences like 「大会の準備をする」 does not mean just to prepare necessary materials (things), but includes the idea that you are managing an organization (event), and can be considered more general (encompassing).
◇「用意」as seen in 「大地震にそなえて十分な用意をする」 and 「当日は上履を御用意ください」puts the focus on collecting (preparing) the necessary goods (materials) in advance.
◇Also the very similar 「支度」is used for the specific action you are doing in order to prepare the necessary materials (things). 「支度金」 is the money used to buy the necessary goods (materials) > and 「食事の支度をする」means to collect the necessary goods and prepare food.
So, 準備, 用意 and 支度 are similar. 覚悟 can be considered different from the above, as it means "mental preparation for a dangerous, difficult or disadvantageous situation".
