How do you add text wrapping to a cell using OpenXml when creating excel files?

You need to define styles for this. Styles are defined inside a stylesheet. Each style has an ID and when you create Cells you can refer defined style ID.

Defining stylesheet for the spreadsheet:

private WorkbookStylesPart AddStyleSheet(SpreadsheetDocument spreadsheet)
{
    WorkbookStylesPart stylesheet = spreadsheet.WorkbookPart.AddNewPart<WorkbookStylesPart>();
    Stylesheet workbookstylesheet = new Stylesheet();

    // <Fonts>
    Font font0 = new Font();            // Default font
    Fonts fonts = new Fonts();          // <APPENDING Fonts>
    fonts.Append(font0);

    // <Fills>
    Fill fill0 = new Fill();            // Default fill
    Fills fills = new Fills();          // <APPENDING Fills>
    fills.Append(fill0);

    // <Borders>
    Border border0 = new Border();      // Defualt border
    Borders borders = new Borders();    // <APPENDING Borders>
    borders.Append(border0);

    // <CellFormats>
    CellFormat cellformat0 = new CellFormat()   // Default style : Mandatory
    { 
        FontId = 0, 
        FillId = 0, 
        BorderId = 0 
    };
    CellFormat cellformat1 = new CellFormat(new Alignment() { WrapText = true });          // Style with textwrap set

    // <APPENDING CellFormats>
    CellFormats cellformats = new CellFormats();
    cellformats.Append(cellformat0);
    cellformats.Append(cellformat1);

    // Append FONTS, FILLS , BORDERS & CellFormats to stylesheet <Preserve the ORDER>
    workbookstylesheet.Append(fonts);
    workbookstylesheet.Append(fills);
    workbookstylesheet.Append(borders);
    workbookstylesheet.Append(cellformats);

    // Finalize
    stylesheet.Stylesheet = workbookstylesheet;
    stylesheet.Stylesheet.Save();

    return stylesheet;
}

Now when you add cells, use the defined style ID as follows:

// Assign our defined style with text wrap.
Cell c1 = new Cell(){ StyleIndex = Convert.ToUInt32(1) };

EDIT: You need to add stylesheet after adding workbookpart.