I'm gonna assume you're working with Gamemaker.

Draw a string on the screen that describes the objective, for example: "Survive 60 seconds" or "Colect coins"

If it's time based:

Program a timer, GM has built in alarms that are easy to use , but you still have to display the time and remember to set it. If you need help with alarms watch THIS

If it's collectible based:

Have a collectible that disappears when the player touches it. Then have a code somewhere that checks if collectible exists or not. 

if !instance_exists(collectible_instance) 

{

            //end game/ win/ add points 

}

If you want to have a list of objectives use an array or stacks to keep them grouped and then execute objectives one after another. 

With ds lists you could shuffle all the objectives around and have them sort of randomized which could be cool in some contexts.