To avoid the player getting lost in a game some game needs to remind the player what he is doing. Most common in role playing games where the player can have any number of quest spread out all over the world. Ex of the games listed for each way of doing things.
Current Objective :
In games where there is one goal at the time such as a shooter it works by listing the objective on the screen. Or only show it when it changes and add a button for the player to show it if he forgets it. Optional objectives can also be listed in the same screen if the game haves them. This system works best when there is a single objective and when it's done or fails there is a new one. Add a marker on the screen where the player needs to go to complete it and you are done.
Book : Morrowind
This system keeps the log of quests in something that often looks like a book. Each time you do something on a quest the last page of the book is updated with the progress. This works great for the first page and then 10 hours in you have 100 of pages and trying to find uncompleted quests is a nightmare. Let this system die.
List: Skyrim
This list all the quests in two list, one for completed and one for active. Both sorted in order of newest changed ones. Clicking on a quest shows the current objective.