One of the major issues in transporting water long distances via canals or other means for agriculture is salinization. This is particularly evident in large parts of the former Soviet Union, particularly where large amount of water were diverted from the Aral sea. Not only is the exposed sea bed a toxic wasteland of salt flats from the water evaporating away, but the large areas irrigated by canals have also become heavily contaminated by salt through the process of salinization. (The incredibly poor agricultural practices of collective farming, unrestrained use of fertilizers and pesticides didn't help either).
Aral sea, before and after
So the conception of open air canals along Mars, lined with lush agricultural fields and forests (hence their discovery by human astronomers in the 1800's...) is sadly wrong headed. Unlike the Nile River, which floods the banks of the river and the delta, flushing away salt build up and renewing the soil with fresh silt, canals will have a slow and relatively constant flow of water.
Romantic conception of the Martian canals
So how will the Martians survive? The best way to deal with this is to transport the water from the poles to the agricultural zones through pipelines, where the water is segregated from the soil. The water is also protected from environmental contamination (i.e. dirt, pathogens or agricultural runoff) entering the stream, until it reaches its destinations.
Typical water pipeline from the Great Lakes to a mid sized Canadian city. This is one of at least 4 pipelines (from two separate lakes)
The Martians can choose to store the water in whatever system is suitable, such as artificial lakes, pumping it into sub surface aquifers or building giant cisterns to hold it until needed. In order to utilize the water for agricultural purposes, the best method for long term conservation of soil (particularly given the equatorial climate is warm and dry) is to use "trickle" or "drip" irrigation. Here the water is pumped through permeable pipes laid along the rows of crops and water literally drips out of the pipe into the root systems of the plants. This conserves water, by precisely metering it to the plants, and minimizes the salinization of the soil in the longer term.
Drip irrigation in the field
Israeli farm from the air. The Martian farms can look like this
The other major issue is the energy required to do all this. A system of pipelines will need "melting stations" at the [poles to turn the ice into liquid water. The water then needs to be pumped up to 5000+ km from the poles to the farmlands in the equatorial zones, then processed for Martian consumption, or pumped through the network of drip pipes into the fields. Extra energy will be needed to pump water into and out of storage (if artificial lake are carved into hilltops, water can flow to the end user via gravity, but you still need to pump it into the lakes first).
Solar mirrors over Mars. You need energy on this scale for the project to work
The Martians can use nuclear energy, solar power, geothermal energy or whatever else is common in your setting. The energy source needs to be reliable and large scale, much like the baseline energy grid on our world.