Well you put the adsense code just before your body tags close for example

<script>
bla bla

bla bla

bla bla boop

</script>
</body>

Google uses an external javascript file so you wont need to worry about your host accepting javascript most do anyway.

As for your second question I'm assuming you dont want it actually embedded in your page more of a sub folder so:

http://www.yourdomain.com/blog/

You can use blogger and get a sub domain from them at:

http://www.blogger.com

Or if you want it hosted on your actual site with more control most of the members here including lisa who has recently upgraded to Wordpress would recommend it however like blogger they also have a version where you can use them as the host.

You can download Wordpress for your site and host it via your site

http://wordpress.org/

Or

You can sign up just like blogger but a different company at here for a free Wordpress sub domain and hosting by them.

http://wordpress.com/

For installing once you have download and unpacked your files from Wordpress need to be uploaded into your chosen sub folder or sub domain folder via FTP which im sure your familiar with.

So for you it probably will be:

http://www.yoursite.com/blog/

Replacing 'yoursite' with your actual domain name of course use the quick install guide that they provide for proper instructions to install this great app and web software.

http://codex.wordpress.org/Installing_WordPress

I recommend the famous five minute installation as its by far the quickest and simplest but if you want to take it slower that's fine too!

Once you've installed your word press you will have to go through multiple set-up questions such as database information when running the set-up script when you are instructed to do so, so make sure to have your MySQL database login, name and server at hand!

If you have any problems installing it just post here and im sure we will be able to help you out!

Oh and Good luck!

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