D&D5 has only 3 levels: Dark, Dim or Light.
In the absence of a light source it's Dark - take this as the default state for underground and nighttime. Start with everywhere is dark; If you are in the dark you are effectively blinded.
To remember: Write "Dark" prominently on the map.
To make an area Light you need a light source, blindsight or darkvision.
The sun is a good one; if it is daytime and you are outside or inside but with decent sized windows/doors its light, as a rule of thumb Light will go about 20 feet inside; Dim another 20 feet; after that it's Dark. Most above ground buildings will not be big enough or opaque enough to be dark. Therefore, Darkness only matters either a) at night or b) well inside (e.g. underground).
To remember: Write "Day" and "Night" on a piece of card and put it right way up on the map for aboveground adventures.
As DM you can create other natural light sources: lava, phosphorescence etc. These will be relatively rare and therefore memorable in their own right.
To remember: Write prominently on the map where these special natural light sources are and sketch the areas they illuminate as "Light" or "Dim".
The rules for artificial light are given in the PHB. Someone is either carrying them (in which case the area around the carrier is illuminated) or they are fixed in a position (in which case someone needs to maintain them).
To remember: Write prominently on the map where fixed artificial light sources are and sketch the areas they illuminate as "Light" or "Dim".
To remember: Get some rigid clear plastic (the covers on women's shoe boxes is what I am thinking of). Cut them into the shape of the light source at the scale of the map (60-foot circle for a torch, 120-foot cone for a bullseye lantern etc.). Mark the boundary between "Light" and "Dim". Cut a hole in them for a miniature to fit through if you want. Drop them on the map and move them around.
Consumption Most artificial light sources don't last forever. A torch, a Light cantrip and a Daylight spell lasts an hour, a pint of oil 6 hours etc.
To remember: You need to track time - if resources are not an issue you do not need to be precise - a party adventuring for 24 hours underground will be active for about 16 - they will use 18 torches or 3 pints of oil per day, this allows for the "overlapping" time where two are lit at once. This is generally close enough. You see the value of the light cantrip - too bad if the only PC that can cast it gets incapacitated while 3 miles underground (evil grin).
To remember: Good tactics for monsters with darkvision or blindsight is to target the light source - extinguish the torch or cover the light cantrip object.
Darkvision provides the equivalent of dim light and is black and white only. Most monsters and Demi-humans have this; humans don't. Dim light imposes disadvantage on Wisdom (perception) checks.
To remember: If your party/monsters consist solely of creatures with darkvision, then everywhere within range is dimly lit. If they want to find things though they will still need a light source or else deal with the disadvantage.
These creatures don't see and don't need light to operate
To remember: This is generally limited by range. Outside that range they rely on normal vision, if they have it.
As discussed in How far away can you see light?, most of the time we use the modern scientific interpretation of seeing. That it is reflected light falling on your retina that allows you to see. Therefore, it is the lighting on the object being seen that matters.
In a fantasy game of course; it doesn't have to be that way. As the PHB says, if you are in the dark you are "effectively blinded". You can take this as written and say that if you have no darkvision and are standing in the dark then you can't see anything even if that object is illuminated. That would be ... strange, but maybe also fun. Note that it seriously disadvantages humans over the other races.