Depending on how used to human contact your chickens are, the easier or harder it will be to catch them. A little enticement with a handful of pellets should get them close enough!
As a rule the best way is to quickly grab their feet from under them. Do NOT chase your chickens around grabbing at their tails or wings. This will only cause them panic which could be bad for their health or at the very least, affect egg production.
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Anonymous2009-04-01 4:37
Sometimes your chicken may think that you are a cockerel and flatten themselves to the ground in anticipation of mating. This will actually make them easier to pick up!
Once you have your chicken by the legs try to get it into a position in which you can carry it whilst supporting its body. Use one hand to support it from underneath by putting your index finger between its legs and securing the legs with your thumb and forefinger.
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Anonymous2009-04-01 4:37
With one hand under the chicken, it is relatively easy to keep the chicken quiet and do any healthchecks you need to. Handling your chicken and getting it used to human contact will help you in the long-run even if you aren't keen to pick it up simply to stroke. You may want to put it in the eglu in a hurry before leaving the house, and a willing chicken will make life much easier!
As you can see from the pictures there are two ways you can carry your chicken easily, head forwards or head backwards.