The short answer to this question is unfortunately, there is no simply way to tell the difference between a male and female robin. Even experienced ornithologists and ringers with many years of experience admit that distinguishing between male and female robins by their appearance alone is near enough impossible. The only definitive way to tell them apart is by a DNA test.
However, this doesn't mean that it's completely impossible to identify whether it is a male or female, as certain behavioural traits can help give an indication but it's not always 100% reliable.
It's common for a lot of people to see two robins together in their garden at any one time and the reason why this is such a popular question. If you have, then chances are it will have been a male and a female. This is because male robins are notoriously territorial with the female robin only entering the males territory during the breeding season.
On average, male robins are generally larger in size but this isn't always the case. Female robins will often be larger than males whilst carrying eggs.
The peak of the head can be a small but distinguishable feature; females tend to have more of a 'V' shape whilst males have more of a 'U' shape. This only becomes apparent when looking from above, so it's not something that you can generally use as a factor to tell a male and female robin apart.
During the breeding season, usually between March and August, part of the mating ritual is for the male to feed the female. If you're lucky enough to witness this, you'll be able to tell the birds apart, as the male will be feeding the female.
Female robins are the nest builders and also the ones to incubate the eggs. The males will sit nearby to protect the eggs and of course their territory.
Robins are extremely territorial and means that females will only enter territories during the breeding season with the male generally holding territories all year round. If you come across a noisy and aggressive robin outside of the breeding season, it's more likely to be a male than a female.
Many people think that you can tell the difference between male and female robins by the intensity of the colour on their breast. It's thought that male robins have a much brighter red breast than the female. Recent spectrometry studies have somewhat confirmed this, although, it's pretty much impossible to tell the difference when just comparing two robins as there is considerable overlap between the sexes.
Many people think that female robins don't have red breasts when in fact they do. Juvenile robins are the ones who lack the red bib. It's also thought by many that females are the only sex that have white bars on their wings but again, this actually isn't true as the males also have these.
Statistically speaking, it's more likely that you've seen a male in your garden than a female. This is also true during the breeding season as garden populations tend to be more abundant with males' populations.