As a general rule preschoolers love stories that they can participate in. For this reason storytelling makes an ideal basis for a counting lesson. Read a story aloud with a group and give them the opportunity to count different things from the pictures in the book. Let them shout out the number of certain objects as a group as well as picking individuals who put their hands up to count out the number of objects. Try to introduce the idea of bigger and smaller numbers through stories. For example you might introduce six frogs who have five lily pads, and ask the children if they have too many lily pads, too few or just the right amount. For older children extend this idea by improvising a story and have the children take turns to pick what happens next in the story. Explain to them that each suggestion must contain a number of objects or characters; for example they might suggest that "six zebras turn up to join the party" or "the animals find a house with 10 doors."
One of the best ways of helping children to learn numbers in sequence is through songs. There are songs to help children learn to count both forwards and backwards as well as songs which involve things such as skipping forward two numbers at time. Keep the speed slow while the children learn the songs and slowly speed it up as they become more proficient.
Learning math is all about learning how to extract the essential, abstract properties from a whole range of situations. Categorizing things by numbers is an ideal way to develop this skill. Set up a number line on the wall and get children to sort toys or other objects according to the number of legs, wheels, eyes, etc. As they get more familiar with the activities give them more complicated tasks, like finding the objects with the most of something and the least of something. Finally allow them to decide how to categorize the objects themselves, but make sure that they are counting correctly.
Many children find it hard to learn while stuck sitting down, so they may welcome counting tasks involving running around. One example is getting the children to run around, and then hurriedly form groups of the number you call out. Another is to write the numbers very large on the walls of the schoolyard in chalk and getting the children to run to the numbers that you call out. Later, replace the numbers themselves with different-sized groups of objects. You can also try calling out: "Animals with four/two/no legs!" and having them move about like animals with that number of legs.