Try to improve your soil: Often because of moderate soil quality or clay soil, water becomes difficult to pass. In order, to keep the drainage system active, you need to focus on your soil quality which should be rich and loamy. Already damp areas take the time to evaporate rain or sprinkler water, making the plants vulnerable to diseases. If you have foliage in your garden, diseases may attract quickly. The only solution, in this case, would be improving the soil quality and air circulation. You may consider digging a lot of organic manure which helps to retain excess moisture underground.
Create raised beds: Raised beds control soil in it, and thus drainage becomes easier. Soil keeps up with its nutrition and does not flood away with water. Problem solved!
Add water loving plants: If not a good drainage system, you can grow some water loving plants that can easily survive in lots of water. Ferns, mint, and maples are some of the plants that can survive in water.
Create a channel to let water pass: You can add gravel channel as a dedicated route to pass water from your garden. However, ensure that the channel is well made and release in an area where neighbors or others are not disturbed. You can send them directly to the street or gutter. If gravel route does not work, you can turn to plan B and dig a hole filled with gravel.
Employ drainage tiles if the problem is severe: If water-logging appears, you can install drainage pipes or French drain systems which are pretty expensive, but will give you a good result for a longer duration.
Simply route water flow: One of the effective ways to direct the water flow is by taking a shovel or trowel and creating a diversion channel. One or more channels can be set up without paying a penny, and your problem will be solved in minutes.
Perforated plastic pipes that can ease your problem: A PVC pipe can be utilized by digging lots of holes. Only bury them lightly or deeply under the soil to let the water divert to your required location. You will get PVC pipes at the local supply stores, but make sure that you buy large and light tubes which are easy to install and move.