Ok this is real easy
Get yourself a digital volt meter one with min/max will make your life easy
Step one: Charge battery over night (assuming you do not own a 30 amp+ charger)
Test battery voltage at the battery posts, yes it is located in the &%#@ trunk. Clean the battery posts while you in there. Clean the battery ground cable connects too. Remove and clean the positive jump point under the hood. NOTE: disconnect the negative cable at the battery while doing all the cleaning mentioned.
Q? Reads over 12.4v? Proceed to step 2-4
Step 2: Read battery voltage with the engine at idle for 15/20 secs
Step 3: Read voltage at 1500 rpm same time
Step 4: Read voltage at 2500 Rpm same time

You are looking for fluctuating voltage at any rpm. Vehicle should display 13.2-14.7 constant voltage. And drop while the engine running is a volt reg going bad as the contact internally is lost (brushes). Turning on a few accessories will help pin any volt drops.

Replace alt with a new unit not a parts store reman unit. See one of vendors like ECS etc for quality units. Anything over 10 years is on borrowed time.
There are lots of postings on rebuilding your current unit if you have the DIY skills and time.

Helpful?

__________________

2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green