Are you sure that your printer doesn't have two paper sources? My printer has a conventional sheet fader (where the paper stands almost vertically) but there's also a drawer at the back of the printer for an alternative paper source. There's a button on the front of the printer which toggles between the two paper sources. If it's in the wrong position (i.e. for the empty drawer), I'll get an 'out of paper' message even though I can see that there's plenty of paper in the visible sheet feeder.
If your printer is checking the correct (or only) paper source, there could be a fault with the micro-switch which senses the presence of the paper. If so, it's a fault which requires the attention of the retailer or manufacturer. However, it might just be that the paper isn't properly loaded. With some printers, it's possible for the paper to rest on a small ledge just in front of the feed rollers, rather than actually touching them. Try taking the paper out and re-inserting it.
If you can sort out the paper problem, the way to check your ink status will vary between printers but the following often works:
Go to your 'Printers' folder. (In Windows ME, that's Start > Settings > Control Panel > Printers. It will be something similar in XP or Vista). Right-click on the icon for your printer and select 'Properties'. Exactly what you do from there on varies between printers but you usually click on a 'Maintenance' tab and look for something like 'Status Monitor'.
I'm sorry that this is all a bit vague but you've not stated which printer you're using, so it's hard to be precise.
Chris