There's a few issues with what you've posted. The input document has "&" symbols in it. This will cause problems for parsers potentially. They should show up as escaped characters "&", so I've corrected those.
The primary reason your transformation will not work properly is because your document is in the default "xmlns="http://www.mywebsearch.com/services/catalog" " namespace, but your transformation is trying to apply-templates on nodes that are in no namespace.
This can be corrected 2 ways. Since you're using XSLT 1.0, you can match nodes using the local-name() function to make it namespace agnostic. (eg. match="*[local-name() = 'Products'] ). Or in your transformation, you can assign the default namespace a dummy prefix and use that in your transformation. The later is what I corrected and did in your document. (If you were using XSLT 2.0, there are easier ways to do this.)
This obviously doesn't produce something that is along the lines of what you want, but you now know why it wasn't doing anything at all. You should be able to figure more out from here.
Document
Code:
<ProductResponse xmlns="http://www.mywebsearch.com/services/catalog">
<Products totalResults="2000" includedResults="10">
<Product id="1539555448" categoryId="499">
<title>Apple iPod touch 8GB (3rd Generation)</title>
<description>Up to 1,750 songs UP to 10 hours video Audio Playback: Up to 30 hours Video Playback: Up to 6 hours Earphones, dock adapter, USB 2.0 cable 4.3 x 2.4 x 0.33 inches</description>
<manufacturer>Apple</manufacturer>
<url>http://www.mywebsearch.com/appleipodtouch8gb3rdgenerationpid1539555448/compareprices__rfaf1__af_assettype_id10__af_creative_id6__af_id37427__af_placement_id1.html</url>
<Images>
<Image ysize="60" xsize="60">http://mysearch.com/resize?sq=60&uid=1539555448</Image>
<Image ysize="100" xsize="100">http://mysearch.com/resize?sq=100&uid=1539555448</Image>
<Image ysize="160" xsize="160">http://mysearch.com/resize?sq=160&uid=1539555448</Image>
<Image ysize="400" xsize="400">http://mysearch.com/resize?sq=400&uid=1539555448</Image>
</Images>
<Skus>
<sku>0885909313013</sku>
<sku>12510109</sku>
<sku>885909313013</sku>
<sku>MC086LL/A</sku>
<sku>MC086LLA</sku>
</Skus>
<relevancy>2412893567975424.000000</relevancy>
<Rating value="4.28">
<Image ysize="13" xsize="80">http://mysearch.com/site/rating_4_and_half_star_80x13.gif</Image>
</Rating>
<PriceSet>
<minPrice integral="14299">$142.99</minPrice>
<maxPrice integral="24165">$241.65</maxPrice>
<stores>17</stores>
</PriceSet>
</Product>
</Products>
</ProductResponse>
Transformation
Code:
<xsl:stylesheet version="1.0" xmlns:tns="http://www.mywebsearch.com/services/catalog" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:msxsl="urn:schemas-microsoft-com:xslt" >
<xsl:output method="html" />
<xsl:template match="/">
<html>
<body>
<xsl:apply-templates select="/tns:ProductResponse/tns:Products/tns:Product"/>
</body>
</html>
</xsl:template>
<xsl:template match="/tns:ProductResponse/tns:Products/tns:Product">
<table>
<tr>
<td>
<xsl:value-of select="tns:title"/>
</td>
<td>
<xsl:value-of select="tns:description"/>
</td>
</tr>
</table>
</xsl:template>
</xsl:stylesheet>