1. What is the available supply voltage?
2. What type of input signal? DC? Push buttton?
3. What triggers the timer?
3. What type of solenoid? Part number? Volt/current rating?
4. Latch output?
5. Solenoid reset requirements?
The circuit below is one way to do it. Please note this is provided as a reference only. As others have mentioned, we need to know what voltage you can supply the circuit with as well as the voltage and current rating of the solenoid.