There are a lot of tutorials on Wordpress as well as tables in general, Wordpress uses the same table format as standard HTML so any tutorial on using tables in web page design will work. Here's a good general purpose table tutorial - http://fastwebstart.com/html5-table/
To create or edit tables it is best to use a combination of the Visual Tab and the Text tab in the Wordpress editor. The Text tab is for entering and editing code directly.
There are also many great table plugins for Wordpress to make it easier. Probably one of the best for heavy duty use is Tablepress - https://wordpress.org/plugins/tablepress/ With Tablepress you can enter tables manually, import from a webpage or import for a HTML, CSV, JSON, or Excel file. It works beautifully. It also lets people search your table and even sort ir and such (if you select that option).
For your purposes I think there are two fairly straight-forward ways to do it, and without having to reformat each table from scratch.
I think the reason your table did not look correct in Wordpress is because of one or both of these things:
Firstly Wikispaces has it's own style sheets which are not copied when you paste directly into the Wordpress editor's Visual tab.
And secondly you want to use a theme that allows you to select a full page format or turn off sidebars for certain pages (or all pages). You can see that you have a Search bar in the right column which is part of the right sidebar, so Wordpress is keeping that space for sidebar widgets and squashing your table.
What I would do, so as not to have to reformat or re-create the entire table is to look at the source code of the page with the table on it (in Chrome right-click and select 'view page source') and find where it starts with the "<table" tag - copy from before this tag to the end of </table>. So copy all from <table to </table>.
From here you could:
A) Paste this into the TEXT tab of Wordpress' editor, and it may help to make sure that the page you are pasting it into has a full page or 'One Column, No Sidebar' template selected. I did a quick demo for you here - http://hmienterprises.com/demoinstall/27-2/
B) Another way is to take this code and paste it into notepad or another text editor, save it with the .htm extension and then use Tablepress. Go into "Add New Table", go over to the Import tab and choose the file you saved, select HTML beside "Import Format" and let it create a table. You probably want to turn off 'Enable pagination of the table' so it doesn't try to make the table multiple pages. Here's a demo of that - http://hmienterprises.com/demoinstall/37-2/
Unfortunately any links to docs or images on your wiki will still have to be fixed.
An easy way to fix this without retyping each link would be to grab the table code as I outlined above, paste it into a notepad as I mentioned. Then go to Wordpress and upload all of the documents and graphics into Wordpress all at once, after uploading click Edit beside one file and look at the File URL and copy out everything in front of the filename (including the / right before the filename). Now go to your notepad and find the references to Wikispaces (in the case of your page you referenced in your message it would be 'http://www.wikispaces.com/site/embedthumbnail/file/') and use the Replace in your Notepad to replace the Wikispaces URL with the Wordpress URL (make sure it has a / at the end).