The Fly spell grants flying movement. How you use that movement is entirely up to you
The spell Fly grants flying movement:
You touch a willing creature. The target gains a flying speed of 60 feet for the Duration.
Flying movement is described in the Movement and Position section of the basic rules:
Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
When you have flying movement, you are free to move through the air at any altitude you like.
The only limitation is how far you move. You can move through the air up to your flying movement (which the Fly spell grants 60) at any altitude (or change altitude) so long as you do not exceed 60 feet of movement during a turn.
You may, of course, take the Dash action while flying to move 120 feet in this way. Some classes/races allow you to also Dash as a bonus action, which would increase this to 180 feet. And some affects will reduce your flying movement. (Warding Wind spell creates a 10' radius that is treated as difficult terrain, which would effectively halve the movement of a creature flying through it for that distance).
If you have not moved and are standing on the ground, you may fly up to any height that is less than or equal to your flying movement (ignoring the Dash action).
You continue to fly and may fly back to the ground as long as the spell is affecting you and, crucially, you do not get knocked prone. If the spell ends or you are knocked prone, you immediately fall and, if you are high enough (>10 feet), take damage.