Done it like below to implement Tab key functionality to move from one cell to another. Moreover, to create a border around selected cell(on cell click/Tab key press) and selected row(on RowSelector click).

<style type="text/css">

 tbody>tr>td.igg_SelectedCell, tbody>tr:hover>td.igg_SelectedCell {

   background-color:white;
   border-bottom: 0px solid #000;
   border-top: 0px solid #000;           
}
tbody>tr>td.igg_SelectedCell[aria-selected=true] {
 border: 1px solid #000 !important;
}

tbody.igg_ItemWhiteBorder1>tr>td{

 font-size:8pt; font-family:Verdana; background-color:white; text-align:left; vertical-align:middle; text-overflow: ellipsis !important; border-right:1px solid #fff; border bottom: 1px solid #fff;

}

<style>

<script type="text/javascript">

$(document).ready(function(){
    $('#<%=hfIsRowSelectorClicked.ClientID%>').attr('value','0');
    });

function rowSelectorClicked(){

  $('#<%=hfIsRowSelectorClicked.ClientID%>').attr('value','1');

}

function uwgRD_EnteringEditMode(grid,eventArgs)

{

  if(document.getElementById("<%=hfIsRowSelectorClicked.ClientID%>").value == '1')

{

     if($('table tr td').hasClass('igg_SelectedCell')){

         $('table tr td.igg_SelectedCell').css("border-bottom","1px solid black");

         $('table tr td.igg_SelectedCell').css("border-top","1px solid black");

         $('table tr td.frstChild').css("border-left-color","#fff");

         $('table tr td.lstChild').css("border-right-color","#fff");

    }

  if(document.getElementById("<%=hfIsEditMode.ClientID%>").value == '1')

       eventArgs.set_cancel(false);

else

      eventArgs.set_cancel(false);

}

}

</script>

Defined grid like:

 <asp:HiddenField ID="hfIsRowSelectorClicked" runat ="server" Value ="-1" /> <asp:HiddenField ID="hfIsEditMode" runat ="server" Value ="-1" />

<ig:WebDataGrid ID="uwgRD" runat="server" AutoGenerateColumns="False" Width="750px" AltItemCssClass="AltRows" 
HeaderCaptionCSSClass="igg_HeaderCaptionWhiteBorder" ItemCSSClass="igg_ItemWhiteBorder1" DatakayFields="Id> 
<Columns> 
 <ig:UnboundField DataFieldName="UserName" Key="UserName" CSSClass="frstChild"></ig:UnboundField>

 <ig:UnboundField DataFieldName="EName" Key="EName"></ig:UnboundField>

 ......

 <ig:TemplateField Key="Delete" CSSClass="lstChild">
 <ItemTemplate>
 <asp:Button ID="btnDelete" onClick="btnDelete_Click" Enabled='<%#(hfIsEditMode.Value == "1")?true : false %>' Text="Delete" />
  </ItemTemplate>
</ig:TemplateField>
 </Columns>
<EditorProviders>
 <ig:DropDownProvider ID="ICP">
 <EditorControl ID="editIC" runat="server" DisplayMode="DropDownList" TextField="ShortName" ValueField="Id"></EditorControl>
 </ig:DropDownProvider>
</EditorProviders>
 <Behaviors>
 <ig:EditingCore>
  <Behaviors>
 <ig:CellEditing Enabled="true">
 <ColumnSettings>
 <ig:EditingColumnSetting ColumnKey="UserName" EditorID="ICP"/>
  <ColumnSettings>
 <EditModeActions MouseClick ="Single" EnableOnActive="True" EnableOnKeyPress="True" />
 <CellEditingClientEvents EnteringEditMode ="uwgRD_EnteringEditMode" />
 </ig:CellEditing>
  </Behaviors>
 </ig:EditingCore>
<ig:RowSelectors Enabled="true" RowSelectorClicked="rowSelectorClicked" />
 <ig:Selection CellClickAction="Cell" Enabled="true" RowSelectType="Single">
 <ig:Activation ActiveRowCSSClass="activeRowCSS" Enabled = "true" /> </ig:Activation>
 </Behaviors>
 </ig:WebDataGrid>

For styling please use our guide - http://www.infragistics.com/community/blogs/engineering/archive/2010/08/25/webdatagrid-css-styling-guide.aspx.

If you need further assistance, please provide a working solution demonstrating the issue. You can zip it and attach it to your next post.

I am looking forward to hearing from you.