How can I give points when someone is standing near an item using Minecraft commands?

Solution 1:

Here is just "an item":

execute @e[type=item] ~ ~ ~  scoreboard players add @p MYOBJ 1
kill @e[type=item]

Or for an item named Apple:

execute @e[type=item,name="Apple"] ~ ~ ~ scoreboard players add @p MYOBJ 1
kill @e[type=item,name="Apple"]

The first command should be in a repeating always active command block and the second in a chain always active conditional.