When plants are starting out, extra love is always good. Each plant has specific care instructions but there are a few rules-of-green-thumb that hold true for most plants.
Don't over-water. You want the soil nice and damp. Not soggy. Definitely not constantly soggy. Let soil dry out before watering again, before the leaves start to droop.
Let in the light. Make sure your new plants get plenty of healthy light but watch them carefully. Sometimes new sprouts can dry up quickly in exposure to intense heat. If they are looking a little sad, give them some cover with an umbrella or a tarp, or move them to the shade for a bit.
You also want to protect your recently-transplanted starts from heavy downpours, high winds, and cold temperatures. A simple frame can be built around the edges of your gardening space with PVC piping or stakes that can be strung with a cloth or tarp. You can also make or buy simple frames for individual plants or groups if necessary.
As you progress, you will develop rhythm and relationship with your plants and know when they need attention.