Here's a Video Tutorial about how to use Soundcloud in your homepage: http://www.screenr.com/uySN
To setup soundcloud on the homepage, you have several options but here's 2 easy options:
1) Embedding the player into a text area widget
Go to soundcloud.com. follow this FAQ to embed the player. http://help.soundcloud.com/customer/portal/articles/243751-how-can-i-put-my-sound-on-my-site-or-blog-
Once the iframe code is copied into your clipboard, go to wp-admin > appearance > widget.
Drag/drop the TEXT widget into your homepage one or two column zone.
Paste the iframe code into the box. Here's a screenshot: http://d.pr/i/ZzLb
2) Use a soundcloud player plugin/widget:
Install a plugin such as SoundCloud is Gold (see screenshot: http://d.pr/i/I7pK )
Activate the widget then go to Appearance > Widgets and drag/drop the widget in your homepage one or two column zone.