You can update a list item on SharePoint Online using the Client Side Object Model:
using(ClientContext clientContext = new ClientContext(siteUrl))
{
clientContext.Credentials = new SharePointOnlineCredentials(userName,password);
SP.List oList = clientContext.Web.Lists.GetByTitle("Announcements");
ListItem oListItem = oList.Items.GetById(3);
oListItem["Title"] = "My Updated Title.";
oListItem.Update();
clientContext.ExecuteQuery();
}
For creating a new item, use the following code:
List announcementsList = context.Web.Lists.GetByTitle("Announcements");
// We are just creating a regular list item, so we don't need to
// set any properties. If we wanted to create a new folder, for
// example, we would have to set properties such as
// UnderlyingObjectType to FileSystemObjectType.Folder.
ListItemCreationInformation itemCreateInfo = new ListItemCreationInformation();
ListItem newItem = announcementsList.Items.Add(itemCreateInfo);
newItem["Title"] = "My New Item!";
newItem["Body"] = "Hello World!";
newItem.Update();