A window will pop up which has the boxes for you to enter the dimensions you'll need. If the specs are for 4 and 5/8" by 4 and 15/16", then just put 4.625in in the width and 4.9375in in the height box.
You don't have to enter a bleed or slug info. You can uncheck the "Facing Pages" option, and either enter 0 into all the margin boxes or enter whatever you'd like. If you have an image that is to bleed, just pull the picture frame out .125" (1/8) past all the edges.
Is there something not working the way it supposed to?
About the bleed...if you need a bleed it is best to actually set that bleed amount in your new document dialog box (you can adjust it at any time). That way, when you go to print or export, you can simply choose "Use Document Bleed Settings" and it will use that amount. Otherwise, you have to remember what amount of bleed you gave it. Also, you can preview your document with bleed (choosing Bleed Mode from the bottom of your Tool palette), so you can be sure you have enough graphic going to the edge of the needed bleed. If you've given your doc a .25" bleed, but the printer says they only want .125", then you can always define that in the Print dialog box.
A tip on the measurements...if you don't know what a fraction's decimal amount is, let InDesign do it for you...if you need 5/16" margin, type in 5/16 in the margin value and it will convert it to the decimal. If you want to use a different measurement (milimeters, instead of inches for instance), just type in the amount followed by the proper abbreviation (22mm for instance) and it will convert it to the unit of measure you have set in your preferences. I use this for drop shadows...I often want a one or two milimeter offset...I don't EVEN know what that is in inches!