It depends if you want to implement another Page Layout (easy) or a create Visualforce page (harder). If you want to use a page layout, go to Setup->Customize->Accounts->Page Layouts, click the New button. On the next page, select the existing Account layout to clone from, give your new layout a name, and click Save.  From there you will be taken to the Page Layout editor to make changes if you want.

After you save your new layout, then you need to assign them to a user profile to have it show up for a user. From the list of page layouts, click the Page Layout Assignment button. You will get a list of all your Profiles with their assigned layout. Click the Edit Assignment button to change the appropriate profiles to your new layout.

If instead you want to use a Visualforce page, you first have to create the Visualforce page which uses the Account standard controller. I will not go into that process here, you can read the documentation.  Then you need to replace Salesforce use of layouts to use your new VF page.  Go to Setup->Customize->Accounts->Buttons, Links, Actions.  On the line for New, click the Edit hyperlink. On the next page, switch the Override With option to Visualforce Page and select your VF page from the pick list.   If your page doesn't show up under the pick list, you didn't use the Account standard controller for your VF page.