By not killing it. I bet, everyone working longer than 5 days has met enough motivation killers to fill books. Everyone swears, if they have the opportunity, they will do better. But somehow, these killers persist, and those who implement them usually keep thinking, they are better, 'still one of the good guys', etc.
So, in my opinion, the best way isn't not to try to do good, but to avoid to do bad.
EDIT, Amended on Request:
The Long Version
In my opinion, intrinsic motivation is strongly connected to the identification with the work/the company.
Identification comes from to identify, as in 'to make sth identic', so someone who identifies himself with his work tries to have as little differences as possible between 'doing the work' and 'doing the thing he wants'.
Therefore, everything that forces a decision between benefiting The Company/The Team by working and benefiting oneself is a potential motivation killer, and as such, should be avoided.
Some of those killers i encountered are:
Broken Communications: It matters mostly, how and to whom one says something instead of what. The motivation
to do the right thing (ad res) is punished by killing the messenger, laughing at cassandra and publicly executing the atoner.
Signs: a lot of cc, bcc and to in emails, and a discrepancy between things said in meetings and things said in the cafeteria.
Form over Results: It matters mostly, how work is done, not what it produces. The motivation of producing
something of value is killed by not appreciating the thing produced and punishing the production. It is way easier to just produce nothing by following protocol.
Signs: 'facebook blockers', fixed worktimes, desk regulations. (I think Jeff Atwood wrote sth. about 'Furniture Police')
Boredom/Dead End: In this job, when one stays, one misses something, be it the opportunity to learn, to get to a different area
of expertise (e.g. from coding to design) or to get a pay that can provide for a family. And the longer one stays,
the lesser opportunities there are.
The choice is between improving the company and improving oneself.
Signs: everyone is known as 'the X guy', where X is the thing he's done forever.