From wear and tear to abuse by the elements, even the most sturdy of clothesline posts can become loose and shaky over time. The best way to reinforce the foundation of a post is to use concrete on the below-ground area of the post.
Remove any clothesline attached to the post you wish to work on.
Dig around the post. The best way to do this is to use post hole digger. This tool will allow you dig the area in closest proximity to the post with the least effort exerted. A spade or shovel is also fine for this sort of work, but these tools will require you to dig a larger hole as a result of the way they must be manipulated.
Back-fill some of the soil if you used a shovel or spade. Leave a hole that is approximately 6 to 8 inches from all sides of the post. Doing this will reduce the amount of space you need to fill with concrete, but will allow for a sizable base to be poured, and harden, around the base of the post.
Make sure your post hole is deep enough. The post should descend roughly 24 to 30 inches into the ground to be sufficiently stable.
Pour approximately 6 to 8 inches of rocks or gravel into the hole. This will take up some room and also create space for water to drain at the base of the post.
Prepare concrete mix according to the instructions on the bag. It will typically require water, and sometimes sand.
Pour concrete mixture into hole until it is flush with ground level.
Using a level, ensure that the post is standing straight up.
Level concrete with a trowel and slope the outside edges of the base downward so water can drain off. The small size of the hole and the density of well-mixed concrete will hold the pole in place as the concrete sets, but having some braces in place, or a setting box, can help if the pole is very thick. Allow to harden for the appropriate amount of time as the instructions on the mixture dictate.