What is the best way to use an embedded database, say sqlite in Python:
I highly recommend the use of a good ORM. When you can work with Python objects to manage your database rows, life is so much easier.
I am a fan of the ORM in Django. But that was already recommended and you said that is too heavyweight.
This leaves me with exactly one ORM to recommend: Autumn. Very lightweight, works great with SQLite. If your embedded application will be multithreaded, then you absolutely want Autumn; it has extensions to support multithreaded SQLite. (Full disclosure: I wrote those extensions and contributed them. I wrote them while working for RealNetworks, and my bosses permitted me to donate them, so a public thank-you to RealNetworks.)
Autumn is written in pure Python. For SQLite, it uses the Python official SQLite module to do the actual SQL stuff. The memory footprint of Autumn itself is tiny.
I do not recommend APSW. In my humble opinion, it doesn't really do very much to help you; it just provides a way to execute SQL statements, and leaves you to master the SQL way of doing things. Also, it supports every single feature of SQLite, even the ones you rarely use, and as a result it actually has a larger memory footprint than Autumn, while not being as easy to use.