Eric White's Blog

This is getting long in the tooth, but an answer still needs to be there for others. There are some things that are background to cover first. Since you didn’t give much detail as to where you are starting from, you start with building the top level container to add parts to. At an absolute minimum, you need this top level container and a worksheet (can be empty).
You need to add other parts to make this happen. One is the WorkbookPart which is the container to add a workbook to. Another is the WorksheetPart to contain the sheet description. This also requires a SheetData part to build your spreadsheet rows and cells in. The part that will be of help to you is the WorkbookStylesPart that will be the container for your stylesheet. An example stylesheet would look like this below. It has a commented bold style for you to emulate:

        // Style part
        private Stylesheet GenerateWorkbookStylesPartContent(WorkbookStylesPart stylesPart)
        {
            return new Stylesheet
            (
                new Fonts
                (
                    new Font(new FontSize(){Val = 11}, new Color(){Rgb = new HexBinaryValue(){Value = "000000"}}, new FontName(){Val = "Calibri"}),
                    new Font(new Bold(), new FontSize(){Val = 11}, new Color(){Rgb = new HexBinaryValue(){Value = "000000"}}, new FontName(){Val = "Calibri"}),
                    new Font(new Italic(), new FontSize(){Val = 11}, new Color(){Rgb = new HexBinaryValue(){Value = "000000"}}, new FontName(){Val = "Calibri"})
                ),
                new Fills
                (
                    new Fill(new PatternFill(){PatternType = PatternValues.None}),       // Required. FillID = 0
                    new Fill(new PatternFill(){PatternType = PatternValues.Gray125}),    // Required. FillID = 1
                    new Fill(new PatternFill(new ForegroundColor(){Rgb = new HexBinaryValue(){Value = tabColor1}}){PatternType = PatternValues.Solid}), // FillID = 3
                    new Fill(new PatternFill(new ForegroundColor(){Rgb = new HexBinaryValue(){Value = tabColor2}}){PatternType = PatternValues.Solid}), // FillID = 4
                    new Fill(new PatternFill(new ForegroundColor(){Rgb = new HexBinaryValue(){Value = "FFE2E2E2"}}){PatternType = PatternValues.Solid}) // FillID = 5
                ),
                new Borders
                (
                    new Border(new LeftBorder(), new RightBorder(), new TopBorder(), new BottomBorder(), new DiagonalBorder()),     // Default - required
                    new Border
                    (
                        new LeftBorder(new Color(){Auto = true}){Style = BorderStyleValues.Thin},
                        new RightBorder(new Color(){Auto = true}){Style = BorderStyleValues.Thin},
                        new TopBorder(new Color(){Auto = true}){Style = BorderStyleValues.Thin},
                        new BottomBorder(new Color(){Auto = true}){Style = BorderStyleValues.Thin},
                        new DiagonalBorder(new Color(){Auto = true}){Style = BorderStyleValues.None}
                    )
                ),
                new CellFormats
                (
                    new CellFormat(){FontId = 0, FillId = 0, BorderId = 0, ApplyFont = true},   // Index 0 - default cell style.
                    new CellFormat(){FontId = 1, FillId = 0, BorderId = 0, ApplyFont = true},   // Index 1 - Bold.
                    new CellFormat(){FontId = 2, FillId = 0, BorderId = 0, ApplyFont = true},   // Index 2 - Italic.
                    new CellFormat(){FontId = 0, FillId = 3, BorderId = 0, ApplyFill = true},   // Index 3 - Lt yellow fill.
                    new CellFormat(){FontId = 0, FillId = 4, BorderId = 0, ApplyFill = true},   // Index 4 - Lt green fill.
                    new CellFormat(){FontId = 0, FillId = 0, BorderId = 1, ApplyBorder = true},  // Index 5 - Border.
                    new CellFormat(){FontId = 1, FillId = 5, BorderId = 1, ApplyFont = true, ApplyFill = true, ApplyBorder = true}   // Index 6 - Bold w/lt gray fill and borders.
                )
            );              // Return StyleSheet
        }

There are some important things to note: