To change your store's default skin, go to Configuration->Store Maintenance, click on the 'Domains' tab, and then edit the desired store and choose the correct value from the Skin dropdown.
IMPORTANT: When you view a skin, that skin ID is stored in the customer's session data, which in turn is stored in a combination of the CustomerSession & Profile tables. The cookie that your customer will get is ASP.NET_SessionId, which is used as a reference to look up the data in Profile, so every time you return to the site you will see that skin id, even if the DefaultSkinID AppConfig is set to a different value. Remember to clear your cookies when testing to ensure the default skin is being shown. If this is a live site and you are concerned about customers not seeing your new skin, the safest way to proceed is to rename your existing default skin folder (eg. rename skin_1 to skin_10) and put your new skin (when completed) in the folder where your old default skin was. This way you will not have to change your default skin id at all.
Temporarily Forcing a Non-Default Skin
If you wish to preview a skin without changing the default skin id, or set specific customers to view a skin other than the default, you can do so using a querystring parameter appended to your site's URL. If (for example) your site is located at http://www.yourcompany.com and you wanted to preview skin 7, you could go to http://www.yourcompany.com/default.aspx?skinid=7
If you do this for any reason, be sure that the Signin.SkinMaster AppConfig is set the way you wish:
Session - If set to 'Session', the customer will retain the skin you forced them to view after logging in.
Default - If set to 'default', when logging in a customer's skin will be set to the default, regardless of the skin they were viewing the site in before.