Have the correct size baggage
Obey the new security restrictions
Airlines limit the amount and size of carry-on luggage. Also security control at the airport may also limit the amount of baggage that you can take airside and these rules may be different.
Some airlines are stricter than others on the size limitations, although this seems to be more prevalent on very full flights or small planes. For worldwide travel with most airlines and through most airports, you may carry on one bag and one personal item such as a purse, briefcase, or laptop computer. A carry-on bag must fit under your seat or in the overhead bin. Its dimensions should not be more than 56cm x 45cm x 25cm per bag. The exact dimensions do vary with airlines and should be checked.
Also bear in mind that although most airlines do not have weight restrictions on hand luggage, you have to be able to lift it into and out of the overhead locker without help.
Airports apply their own operational policies governing the number of items of hand baggage which may be taken through security. With the exception of the UK, most airports will allow you to carry one carry-on bag and a handbag. In the UK some airports are still insisting on a strict one bag policy (your handbag must fit inside the one bag) so please check.
Do bear in mind that you can buy anything in the shops after the security control and carry that onto the plane but if you have to change planes you will have to go through security control again and the rules will still apply.