To get from central London to Charlton you catch the tube to London Bridge then get a train. You can save yourself a whopping 10p or so and a bit of hassle by getting a One Day Travelcard (zones 1-4). There are 8 trains an hour from London Bridge (platform 1) to Charlton, at the same times each hour.
Drinking options near the ground are severely limited. The usual away fans haunt is 'The McDonnells', just down the road from the station (map). It'll be absolutely heaving with Toon fans from about 12 to kick-off. It used to be a bit of a dive, but it recently had a name change and a re-furb to go with it. An alternative is Charlton Liberal Club, up the hill from the station just past where you turn off for the ground (map). It's a fairly typical club, with big screen TV if there's a Sky game on. The beer's quite cheap, but it'll cost you two quid to get in if you haven't got a CIU card, and it can be hard work getting served. The only other option near the station is probably the Rose of Denmark (map). I think I might have been there about 20 years back, but not since, but apparently it welcomes away fans and has pictures on the wall of visiting supporters. Alternatively you could drink around London Bridge or Charing Cross and catch a last-minute train. A canny pub about a 5 minute walk from Charing Cross is The Chandos. Despite the fancy name it's actually a Sam Smiths pub (ideal for the Tad lads then) and beer's about 50p a pint less than London prices. Click here for a map. Alternatively, there's a Wetherspoons pub about 10 minutes away from the station on Charing Cross Road (map). There are only two direct trains to Charlton an hour, but there are trains to London Bridge every 3 or 4 minutes.
Some sites with more info on the ground, how to get there, pubs, etc are:
Internet Ground Guide
Talk of the Tyne
Addickted.net (excellent site, with pub guide)