We've been relying on a series of soaker hoses attached end to end and snaking through the vegetables. It keeps the water close to the ground and roots without losing it to evaporation. We have a timer set at the faucet that allows us to periodically override it and manually set it to water for about 30 minutes.
The challenge is that now that we've added a flower bed, configuring the hoses efficiently has just gotten more complex.
Last summer we tried growing flowers in large pots to save plot space for vegetables. That meant hand carrying water to each pot on a regular basis.
Pots would be the only alternative for plants like mints, which can take over a garden when planted in the ground.
An approach that has been very successful for my balcony has been plant nannies. A plant nanny consists of a hollow, clay spike that can be punched in beside a plant's roots and a bottle full of water that is turned upside down inside the spike. The water drains slowly as the clay absorbs it and spreads it into the soil.
I use two types. One is large enough to use wine bottles for the water. The other is smaller. It comes with a plastic spike that fits on top of used water bottles. Once the water bottle is filled and the plastic spike attached, it can be turned upside down inside the clay spike.
Another variety uses a globe that fits into the clay spike.
With the smaller version, it's sometimes easy to unbalance the plant. Some experimentation is needed with the plastic bottles. Some won't fit tightly and the water just pours out.
Remember not to put anything but water in the bottles. Fertilizer or other chemicals can clog the sides of the clay spike and keep water from flowing properly.