Most likely a flat or worn out battery. It could be other things, but generally you begin diagnosis at the battery because it's the most common problem and the fastest to rectify. Also pairing an existing parasitic drain or new or re-manufactured alternator or starter motor with a defective battery is generally considered to be urinating into a strong head wind.
E.g. Wasting your time and money. If you can obtain access to one, use a decent 12V charger to charge the battery over night.
If you don't have access to a charger, and are not willing to invest in purchasing one, visually inspect the battery. Is the casing bulging slightly? Is it a maintenance type that you can check the electrolyte levels with?
(as already stated, fill each cell with distilled water until the plates are completely covered. Do NOT fill the cell to the brim). If you're lucky and find a date or date code on the battery, then if it's older than father time, just replace the bloody thing and be done with it.
If it's about three years old or younger, and you live in a temperate climate, perhaps consider taking it to a shop to have it charged and it's capacity tested. Once you have a charged and reasonably healthy battery, then test voltage with the car running. Should be in the ballpark of 13.8-14.5V.
If it's battery voltage and dropping, then inspect your charging system. If it's charging, then turn everything off and do a parasitic draw test. If you don't know how to do one correctly, either look it up or don't even attempt it.
All you will achieve is blow fuses in your multi meter. Depending on what type of vehicle you have, you shouldn't see more than 50-100mA draw when all the doors are shut, key out and left for a few minutes to allow modules like the Body Control Module on some vehicles to go to sleep.