How do I prepopulate fields on a Standard layout?

You can achieve this by passing the values to the standard field id's in the url. This technique is known as Salesforce URL hacking. It is described in detail in this excellent blog post by Ray Dehler.

In this instance, you'd retrieve the standard id of the "Amount" field, and then use this Id in the url to assign a static value to the Amount field. Override the standard "New Opportunity" button to redirect to this url, and you are set to go.

Assuming "opp7" is the standard id of the Amount field, the url will look like:

https://eu1.salesforce.com/006/e?retURL=%2F001D000000rCa6i&accid=001D000000rCa6i& opp7=100

The output is:

Update: Based on the feedback in comments, i've modified the answer to include the standard id. But the id's for custom fields might change from one org to another(Thanks @peter-knoll for pointing that out), you also might want to use this in combination with custom settings as a workaround to hardcoding the ids(which is never a good idea).

Update2: You can also use the API name for standard fields, so instead of using "opp7" above you can use "Amount" in the url. This only works for standard fields though.

Update3: Andrew Fawcett has blogged about an even better and elegant solution for this issue here.

Anup