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The way to create links in HTML is to use an anchor tag with an href attribute to the destination URL as described in these tutorials ...
If you are using Dreamweaver, it will generate that type of code for you as described in these tutorials....
You can make an image clickable and link to another URL by wrapping the anchor tag around the image tag. This is useful for creating graphical buttons or banner ads. If you don't want the link border around the image make sure you use the attribute border="0" on your image tag. Here are some tutorials...
You can create links that opens up your user's default email client with the email address filled it. They are also done with anchor tags, but using the mailto command in the href attribute.
The anchor tags has various additional attributes that you can use. The target attribute as in
target="_blank"
is very often used to create a links that open up in a new window. See tutorials listed here ...
The only problem with that the target attribute is no longer used in valid web pages that are doctyped as HTML 4.0 strict. So if you want to open a link in a new window in standard-compliant way, you have to use the rel attribute along with some javascript as described in the Sitepoint article New-Window Links in a Standards-Compliant World.
You can use other attributes such as tabindex and accesskey to make your links more user-friendly. Also add the title attribute to provide more textual information to screen readers. See tutorial on Accessible Links by HTMLDog.