Google patent - Topic extraction
For keyword selection,
try Google Ad Words - Google Trends

Keyword in URL

First word is best, second is second best, etc.

Keyword in Domain name

Same as in page-name-with-hyphens

Keywords - Header

Keyword in Title tag

Keyword in Title tag - close to beginning
Title tag 10 - 60 characters, no special characters.

Keyword in Description meta tag

Shows theme - less than 200 chars.
Google no longer "relies" upon this tag, but will often use it.

Keyword in Keyword metatag

Shows theme - less than 10 words.
Every word in this tag MUST appear somewhere in the body text. If not, it can be penalized for irrelevance.
No single word should appear more than twice.
If not, it may be considered spam. Google purportedly no longer uses this tag, but others do.

Keywords - Body

Keyword density in body text

5 - 20% - (all keywords/ total words)
Some report topic sensitivity - the keyword spamming threshold % varies with the topic.

Individual keyword density

1 - 6% - (each keyword/ total words)

Keyword in H1, H2 and H3

Use Hx font style tags appropriately

Keyword font size

"Strong is treated the same as bold, italic is treated the same as emphasis" . . . Matt Cutts July 2006

Keyword proximity (for 2+ keywords)

Directly adjacent is best

Keyword phrase order

Does word order in the page match word order in the query?
Try to anticipate query, and match word order.

Keyword prominence (how early in page/tag)

Can be important at top of page, in bold, in large font

Keywords - Other

Keyword in alt text

Should describe graphic - Do NOT fill with spam
(Was part of Google Florida OOP - tripped a threshold - may still be in effect to some degree as a red flag, when summed with all other on-page optimization - total page optimization score - TPOS).

Keyword in links to site pages (anchor text)

Links out anchor text use keyword?

NAVIGATION - INTERNAL LINKS

To internal pages- keywords?

Link should contain keywords.
The filename "linked to" should contain the keywords.
Use hyphenated filenames, but not long ones - two or three hyphens only.

All Internal links valid?

Validate all links to all pages on site.
Use a free link checker. I like this one.

Efficient - tree-like structure

TRY FOR two clicks to any page - no page deeper than 4 clicks

Intra-site linking

Appropriate links between lower-level pages

NAVIGATION - OUTGOING LINKS

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To external pages- keywords?

Google patent - Link only to good sites. Do not link to link farms. CAREFUL - Links can and do go bad, resulting in site demotion. Unfortunately, you must devote the time necessary to police your outgoing links - they are your responsibility.

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Outgoing link Anchor Text

Google patent - Should be on topic, descriptive

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Link stability over time

Google patent - Avoid "Link Churn"

All External links valid?

Validate all links periodically.

Less than 100 links out total

Google says limit to 100,
but readily accepts 2-3 times that number. ref 2k

OTHER ON-Page Factors

Domain Name Extension
Top Level Domain - TLD

.gov sites seem to be the highest status
.edu sites seem to be given a high status
.org sites seem to be given a high status
.com sites excel in encompassing all the spam/ crud sites, resulting in the need for the highest scrutiny/ action by Google.
Perhaps one would do well with the new .info domain class.<update> - Nope. Spammers jumped all over it - no safe haven there. Not so much, now - .info sites can rank highly.

File Size

Try not to exceed 100K page size (however, some subject matter, such as this page, requires larger file sizes).
Smaller files are preferred <40K (lots of them).

Hyphens in URL

Preferred method for indicating a space, where there can be no actual space
One or two= excellent for separating keywords (i.e., pet-smart, pets-mart)
Four or more= BAD, starts to look spammy
Ten = Spammer for sure, demotion probable?

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Freshness of Pages

Google patent - Changes over time
Newer the better - if news, retail or auction!
Google likes fresh pages. So do I.

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Freshness - Amount of Content Change

New pages - Ratio of old pages to new pages

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Freshness of Links

Google patent - May be good or bad
Excellent for high-trust sites
May not be so good for newer, low-trust sites

Frequency of Updates

Frequent updates = frequent spidering = newer cache

Page Theming

Page exhibit theme? General consistency?

Keyword stemming

Stem, stems, stemmed, stemmer,
stemming, stemmist, stemification

Applied Semantics

Synonyms, CIRCA white paper

LSI

Latent Semantic Indexing - Speculation, no proof

URL length

Keep it minimized - use somewhat less than the 2,000 characters allowed by IE - less than 100 is good, less is even better

OTHER ON-SITE Factors

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Site Size - Google likes big sites

Larger sites are presumed to be better funded, better organized, better constructed, and therefore better sites. Google likes LARGE sites, for various reasons, not all positive. This has resulted in the advent of machine-generated 10,000-page spam sites - size for the sake of size. Google has caught on and dumped millions of pages, or made them supplemental.

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Site Age

Google patent - Old is best. Old is Golden.

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Age of page vs. age of site

Age of page vs. age of other pages on site
Newer pages on an older site will get faster recognition.

Note: For ALL the POSITIVE On-Page factors listed above,
PAGE RANK can OVERRIDE them all. So can Google-Bombing.