Having one-column layout (the default) and multi-column layout in the same document or same page requires a section break. Columns are a Section property. As Stefan said, if you select the text you want to be in two columns and tell Word on the Page Layout tab that you want two columns, you will get them.

See Sections / Headers and Footers in Microsoft Word 2007-2013 for more.
See also: Working with Sections (or Why Word appears to behave so illogically when you delete or move a section break or How to preserve section formatting when pasting between documents) by Dave Rado, MVP