Over the Winter you should check your hive(s) every month to check that all is well with the Bees. However from April to August you must make weekly inspections to check on the hives health, colony numbers, stores and honey. From April you must be thinking of swarm prevention. This is a natural event however you may not want your colony to split part way through the season as this may effect honey production.
Swarming is a natural process for the bees and you can can take advantage of this to prevent uncontrolled swarms or to split the colony. A good time to split a colony is when you find queen cells being made on one or more frames during an inspection and hopefully this will give each new colony enough time to build up before the main flow of nectar starts.

Start with an External Inspection
Read your previous hive inspection notes before you do anything and then monitor the bees coming and going through the entrance to see if they are carrying pollen into the hive. Next check the ground in front of the hive for signs of dead bees and lastly check the hive and stand for any damage.

Then move on to the Internal inspection
First check the supers - to see if you need to add more supers, always make sure their bees have enough space to store nectar and honey.
Starting from one side of the hive, lift out one frame at a time from the brood chamber inspect it and replace it so not to chill any eggs or sealed brood on it. (If there are frames with no brood on these can be placed to the side of the hive to give you space). A good idea is to mark one side of the top of the frames that way you will be sure to replace the frames the same way round when you put them back.
Look for the Queen - sometimes you wont see her but do not worry if there are fresh eggs around, if some eggs are still upright you know the queen was laying within the last couple of days. Look for larvae, unsealed and sealed brood across the frames.
Look for Drone brood cells and check the egg laying pattern as patchy or excessive drone brood points to a problem with the queen. Check the pollen stores as this is food for the bees and affects the queens egg laying rate. Check Honey / Nectar - The honey arc should be across the top of the middle frames and covering the outer frames.
Check for Queen cells but complete your inspection before removing any just in case you don't find the queen or any eggs.
Check frame and comb condition - for age or damage and replace where necessary. Check for signs of disease such as foul brood, chalk brood, deformed bees, nosema, waxmoth and varroa. Check any medications if being used but do not use these during honey production.
Lastly fill in you hive inspection sheet with tasks for next time and the history so far.