First of all, I want to ask about what spells I know at what levels. At level 1, I know two level one spells (right?). At level two, I know three spells. Now, does that mean I know the two level one spells plus three level two spells or three spells total but I can learn one level 2 spell? Also, for “spell slots for spell level” I’m really confused. Can someone pleas explain these and where they go on the character sheet? My class is sorcerer. Thanks in advance.
The Spellcasting class feature for your class gives you all the details of how you learn your spells. For the sorcerer, you want to pay specific attention to this sub-section (which is on page 101 in the Player's Handbook and in the basic rules):
Spells Known of 1st Level and Higher
You know two 1st-level spells of your choice from the sorcerer spell list.
The Spells Known column of the Sorcerer table shows when you learn more sorcerer spells of your choice. Each of these spells must be of a level for which you have spell slots. For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level.
Additionally, when you gain a level in this class, you can choose one of the sorcerer spells you know and replace it with another spell from the sorcerer spell list, which also must be of a level for which you have spell slots.
If it doesn't make it clear, the number of spells known on the Sorcerer table is your total number of known spells. So at Sorcerer level 2, you will know three different spells, since there's a three on the table. But they must all be 1st level spells, since you don't have any 2nd level spell slots yet (your number of slots are also shown on the table).
Whenever you level up, you can learn a new spell if your number of known spells has increased. That happens at every level early on (it slows down at higher levels). Regardless of whether you got any additional spells, you can always swap out one of your known spells for a new spell if you want to. All your spells must have levels that you have spell slots for. So you can replace a lower level spell with a higher level one, once you've leveled up enough to have access to the higher level slots.
As a level 3 Sorcerer, for example, you'll get your first 2nd level spell slots. You'll know four spells, of which up to two could be 2nd level (one completely new one and one you swapped out one of your 1st level spells for).
P.S. Don't feel discouraged if you get confused by all the different meanings of the word "level". This is pretty widely recognized as one of D&D 5e's greatest misfeatures, as it makes explanations like this one very confusing for new players. The multiple meanings are mostly a legacy of older editions, carried forwards because they're traditional. You'll eventually figure it all out, just have patience.