As a blogger, you have several options:

• singleton blogs — make your own blog (you post content and manage it). Readers may comment only, without changing any part of your post.
• participate in a group/multi-user blogs (partial control on your blog account) -- more contributors post original material. (Examples of group blogs: BoingBoing, Lockergnome, Weblogs Inc.)
• post as a contributor of a comunity blog (you have no control on what is being published) -- anyone can submit materials which are subject to selection and approval by a team of editors(Comunity blogs: Metafilter, Slashdot)

Blogging systems depend on blogging platforms. Options:

• Hosted — by means of a weblog provider (non-techie directed type of blog).

You just sign-up and set up a blog account at a weblog provider. No need to install any programs/hosting accounts/doman names. You have very limited liberty of your actions — strictly limited by the host's rules (some have more permissive rules). In as far as AdSense is concerned, some hosts may offer you the possibility to have AdSense on your blog pages and manage your own AdSense account and others may just manage their own AdSense account — thus you'll have AdSense on your pages but no control over it and no gains.

• Stand-alone platform -- by means of a weblog software (you will have to handle some technical matters).

You need to install weblog software (which you may download) in a web host (free/paid). Then you can customize and improve your weblog upon your wish.

• Remote weblog systems -- may combine some elements of the two above.

You have the possibility either to host the weblog system in a built-in weblog host (in this case, the set up guideline follows that of the host) or use your own web host and domain (you'll have to provide the FTP details to the remote weblog system). No weblog software installation needed. You'll have some control over your weblog, but you cannot customize very many things.

Google's blogging services (Blogger.com) encourage users to open their AdSense accounts and put AdSense on their blogs.

Of course, if you want to make AdSense money with your blog, you should have the possibility to fully manage your own blog, so as to be able to put your AdSense code in it and optimize it as you think is better.