So I'm fairly new and ended up being the Cleric in my also fairly new group. I haven't played a caster before and the book says that at level 1 I have Bless and Cure Wounds. Do I need to assign these to a spell slot or do I have them inherently (not to be confused with a cantrip; I know I'd have to use a slot to cast them)?
Assuming you are a Life Domain Cleric, those are the two spells you get to have prepared for free, in addition to your normal complement. You always have those two spells prepared. In addition, you may prepare a number of 1st level spells from the cleric list, equal to your level + your wisdom bonus, which will give you probably 3 or 4 more. Those spells are not associated directly with spell slots; those are just the ones you have selected to have ready on that day.
You, at first level, have two 1st level spell slots, so twice per long rest, you may choose to spend a spell slot to cast a 1st level spell, and each time, you choose, at the time of casting, which 1 of those 5 or 6 spells you have prepared that you will actually cast using that slot. This does not affect the number of spells prepared; they are all still prepared, and when you use your other spell slot, you may likewise cast any 1 of those 5 or 6 spells with it, including the same one you cast with the first slot earlier.
After the next long rest, you get your 2 spell slots back for casting. You keep your two domain spells (bless and cure wounds) prepared. You may change which other spells you have prepared for that day.
Spell slots are used to power spells. This is separate from the number of spells that you can prepare each day. The "class spells" — cleric domain spells, or druid land terrain type spells, or equivalent — do not count against your limit of spells prepared each day (which depends on your level and spellcasting ability modifier), but you do need to expend spell slots if you want to actually cast one of them.
Preparing Spells versus Casting Spells
You seem to be mixing up the two different game features of casting spells and preparing spells.
Your cleric has a domain, which provides some spells that are always prepared. You don't have to choose them, they are always ready to be cast if you have a spell slot to cast them with. (Bless and Cure Wounds are from the Life Domain spell list). You then choose some more spells from the Cleric Spell List in Chapter 10 of the Players Handbook to have prepared (ready to cast):
You prepare the list of cleric spells that are available for you to cast, choosing from the cleric spell list. When you do so, choose a number of cleric spells equal to your Wisdom modifier + your cleric level (minimum of one spell). The spells must be of a level for which you have spell slots. (Basic Rules page 21)
That means that if you have a Wisdom of 16 at first level (modifier +3) and are level 1, you add 1 + 3 and can thus prepare for casting 4 additional spells beyond your two domain spells. All in all you start your adventuring day with six spells preparerd. While you do have six spells to choose from, you can only cast two on a given day because you only have two spell slots. (You can cast the same spell twice, or cast two different spells once each).
Let's say you chose Guiding Bolt, Healing Word, Sanctuary and Shield of Faith. For your first adventure day. You have those spells, Bless, and Cure Wounds prepared.
On your next adventure day, you could choose to prepare Inflict Wounds instead of Sanctuary, which means that your could choose from the following spells for the two spell slots that you can cast the next day: Guiding Bolt, Healing Word, Inflict Wounds, Shield of Faith, Bless, Cure Wounds.
Your cleric, based on her level, will have a number of slots per day/long rest, that can be cast before the cleric runs out of spell slots. Your first level cleric has two spell slots. At second level you will have three spell available for casting your prepared spells. You still have to choose which spell to cast from the menu of spells that you have selected.
You don't use a spell slot to cast a cantrip. You can cast it pretty much any time you want to.
A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance. Repeated practice has fixed the spell in the caster’s mind and infused the caster with the magic needed to produce the effect over and over. A cantrip’s spell level is 0. (Player's Handbook, Chapter 10/Basic Rules p. 78, italics mine)