There are 3 essential elements in an Agile approach to projects: the backlog, sprint planning, and the standups.

The Backlog

The backlog is a dynamic list of what project stakeholders consider important to the success of the project
We refer to backlog items as deliverables
Project stakeholders are anyone whose opinions about project success matter
Any stakeholder can add any must-have or like-to-have at the bottom of the backlog at any time in the project
The backlog items and order will change based on the team's performance, learning, and the conditions changing outside the team's scope of control
The backlog owners are the people designated to keep the backlog organized
The backlog is organized by the sequence in which things will begin getting done
Things move up on the list if they have functional, business pay-back, lead-time, or political priority
The backlog owners update the backlog every two weeks parallel to sprint planning
The only deliverables they cannot move on the backlog are those the team is working on in the current sprint
Every deliverable on the backlog has a time estimate in effort hours
The total effort hours for the whole backlog is divided by the number of total sprints expected to define sprint velocity
Sprint velocity is the average number of effort hours the team must do per sprint to be on time for the whole backlog
If any of the deliverables have sensitive end-dates, these dates are listed as timestamps on the backlog

Sprint Planning

A sprint is a regular timeframe for work in the life of the project, usually 2 weeks of work
Toward the end of each sprint, the team plans the next sprint
The team is the composition of talent necessary for each sprint's deliverables
The composition of any sprint may vary from other sprints because of the deliverables' requirements
The team first makes sure that each deliverable assigned to that sprint can be completed in that sprint
If any deliverables require multiple-sprints, they get chunked-down into sprint sized pieces
Any deliverable parts that cannot get done in the next sprint get put back on the top of the backlog
Everyone on the sprint team communicates their available effort hours for that sprint
The backlog planning already established the velocity (of effort hours) required for that sprint
Any gaps between committed and required effort hours is addressed by adjusting sprint scope or resources
People self-assign, and when possible, co-assign themselves to sprint deliverables
Those with the most experience with any deliverable are in the best position to volunteer for assignments
All assignments are posted for each deliverable for each sprint (the "sprint board")
The team decides on the time and location of that sprint's standups

Standups

The standup is a 15 or so minute meeting of the sprint team
Everyone communicates whether the status of their deliverables are up to date
Every deliverable is assigned one of 3 possible status conditions
Deliverables are designated as "begun", "ready" (for decision as done), and "done"
Any assignments that are not yet up to date, are gotten up to date
The team discusses whether any "ready" deliverables are "done"
Those that the team agrees are done, are designated with the status of done
Those that are not done, go back to the status of "begun"
Anyone who needs help, asks for it, and those who can help with anything will volunteer to help
Anyone who wants to help anyone else, offers it Notes on any clarifications or resources are kept on the sprint board
If anyone finishes their assignments and still has committed time left, they can start items at the top of the backlog
If someone cannot complete their assignments in the course of a sprint, there is conversation about the possibility of other resources
Every sprint end with conversation about lessons learned from that sprint and implications for future sprints, always keeping the process focused on strengths, successes, and future possibilities