Reducing agents reduce the OTHER species with which they interact, so they must GIVE electrons to the other species (losing them themselves, which = oxidation). That will happen if they "want" electrons less than the other species.
Oxidizing agents oxidize OTHER species (gaining electrons themselves, which = reduction), and will only do this if they "want" electrons more than the other species.
To decide the "agent" you will ALWAYS have to be comparing species. You will compare the reduction potentials (E values) off of the table, recognizing that a large positive E means something likes to be reduces WAY more than hydrogen (the reference compound) and a negative E means it is harder to get that specie to accept electrons than it is for hydrogen.
So...the one with the largest (most positive) E is going to be reduced (oxidizing agent) because it wants those electrons MOST. This could be the difference between -0.24 and -0.04. In other words, neither may be positive at all, but, in this hypothetical example, -0.04 is "more positive" than -0.24, so when these guys exchange electrons the one with the -0.04 value is always going to get them (oxidizing agent) and the other one is always going to give them up, or be oxidized (reducing agent).
Don't memorize this, but it helps to make mental note that they are opposites...oxidizing AGENTS actually get REDUCED and reducing AGENTS actually get OXIDIZED. You have to keep careful mental track of "Me vs. The Other Guy." =)