Steps for Leveling Up a Your D&D Character
1 - First, you gain hit dice (and a corresponding increase in maximum hit points).
This is described for each class briefly under Class Features, and explained on page 15 of the Player’s Handbook (or here in the free Basic Rules):
Each time you gain a level, you gain 1 additional Hit Die. Roll that Hit Die, add your Constitution modifier to the roll, and add the total to your hit point maximum. Alternatively, you can use the fixed value shown in your class entry, which is the average result of the die roll (rounded up).
2 - Almost everything else is shown on the class table in each class description.
For example, page 71 for the fighter or page 113 for the wizard. You can see the charts for the basic classes online for free as part of the Basic Rules.
In the book they look like the chart below.
2A - At certain lower levels you will need to choose a path, archetype or something similar
2B - Check to see if your proficiency bonus increases
Proficiency Bonus goes up at 5th, 9th, 13th and 17th levels. This also increases, and you should make adjustments for, the following:
Attack rolls using weapons you're proficient with (or your “to hit” roll)
Attack rolls with spells you cast (“to hit” with spells)
Ability checks using skills you're proficient in (Acrobatics, Animal Handling, etc.)
Ability checks using tools you're proficient with (i.e. Thieves Tools)
Saving throws you're proficient in (Strength, Constitution, etc.)
Saving throw DCs for spells you cast (explained in each spellcasting class)
2C - Update your class (ranger, wizard, etc.) features
Anything in the features column will be described in the corresponding description later in the section on that class. In general, when these class features improve at higher levels, there will be a note on the table. For example, Druid has "Wild Shape" at level 2 and "Wild Shape Improvement" at level 4.
If any ability scores (Strength, Dexterity, etc.) go up make adjustments to:
ability score mod
ability saving throws
skills
Some features have per-level scaling not mentioned in the chart so be sure to check the descriptions for each of your features. Example: The paladins Lay on Hands feature increases by 5 points per level.
2D - Update number of spells known, spells prepared and spell slots. If applicable, change spells prepared
You can sometimes change this only when you level up. For Warlocks you can change incantations.
Class | Note | Spells Known | Spells Prepared | Spell Slots | Spell Attack Modifier | Spell Save DC | Ability Modifier |
Barbarian | ~ | ~ | ~ | ~ | ~ | ~ | |
Druid | All druid spells | Wisdom modifier + your druid level (minimum of one spell) | PHB p65 | proficiency bonus + Wisdom modifier | 8 + your proficiency bonus + your Wisdom modifier | WIS | |
Paladin | All paladin spells + "oath" path spells | Charisma modifier + half your paladin level, rounded down (minimum of one spell). | PHB p83 | proficiency bonus + Charisma modifier | 8 + proficiency bonus + Charisma modifier | CHA | |
Ranger | Based on ranger level only; PHB p90 | Same as spells known | PHB p90 | proficiency bonus + Wisdom modifier | 8 + your proficiency bonus + your Wisdom modifier | WIS | |
Rogue | If at 3rd level you choose the Roguish Archetype "Arcane Trickster" PHB p97 Uses wizard spells. | Based on rogue level only; PHB p98 | Same as spells known | PHB p98 | proficiency bonus + Intelligence modifier | 8 + your proficiency bonus + your Intelligence modifier | INT |
Wizard | Whatever is in their spellbook(s). 2 spells are automatically added each level. | Int Modifier + Wizard level | PHB p113 | proficiency bonus + Intelligence modifier | 8 + your proficiency bonus + your Intelligence modifier | INT |
2E - Update damage of spells that increase with levels (See 4 below)
2F - Update any other skills
Other examples of values which increase on the chart are the number of cantrips known, the monk's Unarmored Movement, the sorcerer's Spells Known, or the barbarian's Rage Damage.
Also, Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook for free.
3 - Some racial (elf, human, etc.) traits get better.
This is also just something you'll need to look out for. Usually, it's when you have the ability to cast spells — you may get more at a higher level. In other cases, damage increases.
In the Player's Handbook, this only applies to the Drow Elf subrace (spells), Dragonborn (breath attack), and Tieflings (spells). Hill Dwarf gets an additional hit point per level.
As with class features, marking features which scale with some symbol you'll remember on your character sheet might help.
4 - Damage from most attack cantrips goes up at certain points
These are "level 0" spells — they don't use spell slots or preparation and if known can be cast at will. Most damaging cantrips increase in power at 5th, 11th, and 17th character level. This is noted in the spell description, not on the class chart, because it scales with character level not class level (which may differ if you multiclass — see below). If you have cantrips written on your character sheet as attacks, this is good to be aware of when you level up.
It's also important to realize that other spells don't do this. Some spells note that they can be cast using a higher-level spell slot and give what the effect of casting in that way would be. For example, Magic Missile says:
At Higher Levels. When you cast this spell using a spell slot of 2nd level or higher, the spell creates one more dart for each slot level above 1st.
I can see how it'd be easy to interpret this as meaning "2nd character level", but D&D uses "level" to refer to different things (in 5E, character level, class level, and spell level are all distinct). Here it refers to spell level — Magic Missile is a first-level spell, but if you cast it using a higher-level slot, you can create more darts.
From the class chart, you can see that wizards gain 2nd-level spell slots at 3rd class level. A 3rd-level wizard has two 2nd-level slots and four 1st-level slots, and so could cast magic missile six times, with two of those times gaining an extra dart.
In general, except for cantrips, spell damage (or number of targets, or etc.) does not increase as you level up. Instead, you gain higher-level slots, which you can use to cast some spells with greater effect.
5 - Pretty much nothing else changes.
D&D 5E uses a concept of "bounded accuracy", which means that few things scale just for the sake of going up as you level. You mention "level 2 attributes and passives". This isn't a thing. At 2nd level, your attributes stay as you chose originally (unless of course the DM lets you rebuild; in Adventurer's League you can rearrange things at will up through level 4).
Ability scores only increase as part of the "Ability Score Improvement" class feature (or through Feats which grant increases). When you do get to the point where you increase an ability score to the point where the modifier changes, saves and skill modifiers (including passive checks) should be adjusted to match — but this is technically part of the Ability Score Improvement class feature, not of leveling alone.
6 - Multiclassing
If you are multiclassing — mixing and matching between different classes as you level — special rules apply. (See Multiclassing in the Basic Rules.)