This is a combination of personal opinion and what's been drilled into my brain in college "careers" classes.

When -
About a week is a good amount of time to allow an employer to answer your application. If the job application had a "closing date", you may want to wait until just after that date - some won't look at the applications until ALL have been received and that date has been passed, to help prevent the bias of taking earlier applications over later ones.
It also depends on the size of the company. In a larger company, it's likely that HR will weed out which resumes are acceptable and which are no good before the person doing the hiring even sees them. Assuming that HR doesn't look at these until the closing date, they may take 2 or 3 days to go over all the resumes, prepare and deliver them to the specific department, and then 2 or 3 days for that person to go over them as well - and thats assuming they have no other pressing issues to deal with. A week's wait would not not unreasonable. A small company without an HR department may be able to make their decisions in a couple days, but larger companies, especially for competitive positions, may take considerably longer.
You don't want to approach them too early, as they may not have gotten to your resume yet, which (depending on the person) could have them see you as an annoyance, or as being on the ball. Wait too long, and they may have forgotten about you or see you as a procrastinator. It's a bit of a guessing game.
If there is no closing date, I'd assume they begin to process resumes withing 48 hours of receiving them. Without having to work through a batch, the process is sped up significantly. I've had friends that apply online through a multi-part application and are called before they even finish submitting the resume. Other times, they wait weeks before they hear back. Assess the size of the company and make an estimate as to how long to wait before contacting them.

Whom and how
Most often on the job ad, there is some sort of contact for questions, or the name of the person responsible for hiring. That is the person I would contact. Phone is most personal and direct, but an email will do if they don't provide a phone number. If there is no contact information, I'd simply phone the company and ask for HR, and ask if your application has been processed. If not, leave it there, if so, ask for the person doing the hiring. Speak with them, leave a message, or send an email.
In the case of a VERY small company, the best form may be to simply go into the office and introduce yourself. One job I had I did exactly this - it was a co-op job so they'd already talked to my school, but instead of having the school email the resume to HR, I went into the office and introduced myself and handed them a paper version. Of course, some will take resumes strictly by email or online for so this isn't possible, but it's a nice gesture where possible, followed by the phone, and finally email. The more personal, the better. Be sure to dress as nicely as you would for an interview if you chose to go in person!

Good luck! No solid rule here, except to use your best judgement and assess the company you're applying to - should be able to make a reasonably accurate guess as to how long they need to review your resume.

http://www.nassaulibrary.org/bellmore/JobSearchNewspaper.jpg

I've read an article at examiner.com which might serve as your guide on how and when to follow up on a job application:

1. In your application letter, include that you have intention to follow up.
2. Look for someone who is an insider of the company you have applied to. Search online for helpful links or personalities you might know who works in the company you have applied.
3. Be sure that you expressed interest and highlight your qualifications.
4. Try to do some research on the company or organization that you have applied to.
5. If you don't hear anything from the company write an email, or call them. Don't lose hope.

Don't fill out the online job application. I once read something from a hiring manager that said, in so many words, that standard applications stay at the bottom of the pile while the people who bypass the process move to the top of the stack. But if you do fill out the application, I think the best way to follow up is in writing with a printed copy of the application. This is better than calling because chances are you wouldn't be the only one calling to follow up, and you will likely get a canned response from whoever answers the phone. If you follow up in writing (not email) or, even better, in-person, you stand out and show a level of seriousness that most applicants won't.

Buddwaggi I'm saying good-bye. I have asked Mahalo to remove me
I've had the last dominating person tell me HOW I am 'allowed' to
express myself. And voting people 'down' is arrogant and cruel

It's a cheap shot by those who cannot express themselves, or those
who desire to show.. you mean 'little' (pedophiles?) and a very nasty
form of getting rid of any competition. I will not support Rome

Before I go I have an EASTER present for you. Do you like MATH ?
Math is the language of Cloning...an echo. STAR=RATS to tell on you

Jesus=15131=11=2=TWIN Christ=389912=32=Five=E (most common letter)
32=23 in Opposition. Full circle PI (PI-sees/fish the symbol of Christ)
Two fish in opposite directions. Male AND Female (Scorpio-Score-PI eh?)

555=New Wen 32=23=W WENDY in police code.
555=15=6=FOX a good-looking sister. Sister ?! There is No such thing as
a sister !? (the very point) It's ALL about Hymms (HIS interpretations)

Eve was/is again Male. Test tube human, sheep and insect DNA
Eve has cancer because IS Canned-Sir. Crossbred over centuries into the
natural "Daughters of man" Genesis/Gene-E-sis (real live Grown-up Girls)

Snake in Tree-Medical Staff, Cad-do-sis (Hermes/winged) Her-me/Eve-insect
"They do not repent of what they do with their hands" Revelation
Masturbated Beast-U-all-itty (Pre-nuclear Gods/Greeks/MYTHS-war cloning
"Tails of serpents" sperm/666=FOX a Con Artist (Male dominate force clone

His-tour-wrecked-a-me
Celibate women; Nuns, Shakers, maiden ladies have a mere 7% cancer
93% cancer to Mare-raid (overuse of womb, vagina and reproductive organs)

One-hundred-44 thousand sealed into lead covered underground nuclear
shelters. A Real Cherry..No Bull. The "Lost" Atlantis=Ourselves.
Rotting flesh and plant matter with nuclear holocaust creates Crude Oil
Computers-Come-pew-tours. All will pew-up plenty in nuclear fallout
Nuclear-New-and-clear (All living substance must exfoliate/snake)

"The son's of God'S saw the daughters of man were fair, and took them to
wife" Genesis. War clones freed by bomb blasts from science laboratories
kidnapped, held captive and raped the offspring of the original 144 thou
Patriarchal "wife" (Pay-tree-are-kill) All male ever does. Kill body/soul
A Bomb-in-Nation Does Lead to Dis'soooooo-Lay-shun

Mahalo=Ma-Hell-oh!
"I brought my people out of Egypt, to the wicked is given to name
themselves" Daniel 9:15 DAN=DNA echo clone of the Universe. Quite a
parrot for a pack of pirates! ELLEN is a 'wick kid' English name means
"A Lamp to those in darkness" No ellen D'gene-n-err-is (Eve is Male)
Less-bein-is-him is male sexual fantasy Rome-Ants (carnage of insects)

RUTH "To follow a woman" Every wise young daughter has an older wiser
more experienced NAOMI to teach and guide her to wisdom and a kind man
All a Tink-Cur-Belle ever has is a Peter Pan to beller Nay!owe-ME
and a Botox BOA-talks deadly toxic boutulism (Bought-U-line-is-Him)
HUTCHINSON "the work of a cabinet makers son" MA-haul-eh? hauled me off