For the most part, avoid absolute positioning. It takes elements out of the document flow, making it hard to get them to play nicely together. For example, if your main content is absolutely positioned and you have a footer below that, you would have to move the footer manually every time you added content, which is a hopeless situation.
However, with small items like a logo or a menu within a head section, there's a reasonable argument for placing it absolutely. Just remember, though, that if font sizes are increased significantly, these abs;pos elements might start to overlap rather than reflow. So again, use wisely and with caution.
Absolute positioning is mainly useful for placing small items here and there on an occasional basis.
For the most part, if you want things sitting side by side, use floats.