Generally, state laws are written in such a way as to not conflict with federal laws. There are notable exception, like the state laws pertaining to marijuana here in my state of Washington and in several other states.
Minimum wage laws are a more clear-cut example. Every state has to enforce the federal minimum wage of $7.25/hour. In Washington, we have a law mandating a minimum wage of $9.32/hour. There aren't any conflicts because any employer paying the state minimum wage is also paying above the federal minimum wage. The city council of Seattle recently enacted a bill that will raise Seattle's minimum wage to $15/hour by 2021. A Starbucks restaurant in downtown Seattle in that circumstance would have to pay each of their workers at least $15. A few blocks away in one of the suburbs of Seattle, another Starbucks would be able to pay their workers $9.32. There are several states that have the same minimum wage that the federal law mandates, but they couldn't enforce a law that lowers that minimum. (Although they could potentially pass one, it wouldn't be enforceable.)
Most state laws are written to cover situations that federal law leaves open for discussion. Federal laws don't really cover how the Washington State Department of Transportation will pay for the state highway system, so laws were written to create taxes and road-tolls to accommodate. There are federal laws that determine the maintenance policies of the federal (interstate) highway system, but the specific details of the maintenance are left up to the state. The state could decide when to plow the snow off of the interstate, what equipment to use, and who to hire to do it, but the federal government indirectly requires them to create protocols for that by mandating that the roads be made clear as promptly as possible after becoming blocked.