First you should if it is worth trying to change the soil or not. It might be easier to choose plants that are well suited for a clay heavy soil. There are many plants that are well suited to clay.
If you do decide to change or amend the clay soil keep in mind that it takes ample amounts of amending agents. The primary thing you will need is a large amount of coarse sand and organic material. Make a commitment to changing a larger area i.e. and entire flower bed or section of garden as changing only part of the area will make it difficult for plants to adapt.
There is a sandy material known as builder’s sand that works very well. It is very coarse and has larger particles. An organic material should also be very coarse. There are many types of organic material which can be purchased a garden store but make sure you find one that is particularly coarse. Compost is often a good option.
Plan to have equal parts of coarse sand and coarse organic matter on hand to amend the soil. Extra sand can be used if necessary. Bagged materials probably will not be sufficient as large amounts will be needed. Ensure that you begin to work with the clay soil when it is dry. Cover entire area with 3-4 inches of each organic material and sand. Use a tiller if available to work the sand and organic material into the underlying clay soil. Tillers are often available for rent if you do not own one. Over time the organic material will decay and seem to disappear. You may want to check the pH level of the soil to ensure it is adequate for whatever plants you are trying to grow. The organic material will bring additional acidity to the soil. Hopefully this helps.