How do you upload a file to a document library in sharepoint?

You can upload documents to SharePoint libraries using the Object Model or SharePoint Webservices.

Upload using Object Model:

String fileToUpload = @"C:\YourFile.txt";
String sharePointSite = "http://yoursite.com/sites/Research/";
String documentLibraryName = "Shared Documents";

using (SPSite oSite = new SPSite(sharePointSite))
{
    using (SPWeb oWeb = oSite.OpenWeb())
    {
        if (!System.IO.File.Exists(fileToUpload))
            throw new FileNotFoundException("File not found.", fileToUpload);                    

        SPFolder myLibrary = oWeb.Folders[documentLibraryName];

        // Prepare to upload
        Boolean replaceExistingFiles = true;
        String fileName = System.IO.Path.GetFileName(fileToUpload);
        FileStream fileStream = File.OpenRead(fileToUpload);

        // Upload document
        SPFile spfile = myLibrary.Files.Add(fileName, fileStream, replaceExistingFiles);

        // Commit 
        myLibrary.Update();
    }
}

if you get this error "Value does not fall within the expected range" in this line:

SPFolder myLibrary = oWeb.Folders[documentLibraryName];

use instead this to fix the error:

SPFolder myLibrary = oWeb.GetList(URL OR NAME).RootFolder;

Use always URl to get Lists or others because they are unique, names are not the best way ;)

With SharePoint 2013 new library, I managed to do something like this:

private void UploadToSharePoint(string p, out string newUrl)  //p is path to file to load
{
    string siteUrl = "https://myCompany.sharepoint.com/site/";
    //Insert Credentials
    ClientContext context = new ClientContext(siteUrl);

    SecureString passWord = new SecureString();
    foreach (var c in "mypassword") passWord.AppendChar(c);
    context.Credentials = new SharePointOnlineCredentials("myUserName", passWord);
    Web site = context.Web;

    //Get the required RootFolder
    string barRootFolderRelativeUrl = "Shared Documents/foo/bar";
    Folder barFolder = site.GetFolderByServerRelativeUrl(barRootFolderRelativeUrl);

    //Create new subFolder to load files into
    string newFolderName = baseName + DateTime.Now.ToString("yyyyMMddHHmm");
    barFolder.Folders.Add(newFolderName);
    barFolder.Update();

    //Add file to new Folder
    Folder currentRunFolder = site.GetFolderByServerRelativeUrl(barRootFolderRelativeUrl + "/" + newFolderName);
    FileCreationInformation newFile = new FileCreationInformation { Content = System.IO.File.ReadAllBytes(@p), Url = Path.GetFileName(@p), Overwrite = true };
    currentRunFolder.Files.Add(newFile);
    currentRunFolder.Update();

    context.ExecuteQuery();

    //Return the URL of the new uploaded file
    newUrl = siteUrl + barRootFolderRelativeUrl + "/" + newFolderName + "/" + Path.GetFileName(@p);
}

string filePath = @"C:\styles\MyStyles.css"; 
string siteURL = "http://example.org/"; 
string libraryName = "Style Library"; 

using (SPSite oSite = new SPSite(siteURL)) 
{ 
    using (SPWeb oWeb = oSite.OpenWeb()) 
    { 
        if (!System.IO.File.Exists(filePath)) 
            throw new FileNotFoundException("File not found.", filePath);                     

        SPFolder libFolder = oWeb.Folders[libraryName]; 

        // Prepare to upload 
        string fileName = System.IO.Path.GetFileName(filePath); 
        FileStream fileStream = File.OpenRead(filePath); 

        //Check the existing File out if the Library Requires CheckOut
        if (libFolder.RequiresCheckout)
        {
            try {
                SPFile fileOld = libFolder.Files[fileName];
                fileOld.CheckOut();
            } catch {}
        }

        // Upload document 
        SPFile spfile = libFolder.Files.Add(fileName, fileStream, true); 

        // Commit  
        myLibrary.Update(); 

        //Check the File in and Publish a Major Version
        if (libFolder.RequiresCheckout)
        {
                spFile.CheckIn("Upload Comment", SPCheckinType.MajorCheckIn);
                spFile.Publish("Publish Comment");
        }
    } 
}