Ok so pretend I'm 5 and have no prior knowledge of how the US economy works.

I’m an idiot so I feel qualified to answer this.

When you raise interest rates you make less people borrow money and more people save money. This takes money out of circulation which will lessen inflation.

Every American adult should watch "How the Economic Machine Works" by Ray Dalio, who runs Bridgewater.

It's 30 minutes, but it's entirely worth it. A high school kid could understand this video; it explains how the economy works in simple terms.

LINK

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1) How does raising Interest rates reign in already High inflation on product goods? What should be the goal we(fed) want to achieve here? What should we expect?

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Law of supply and demand. If demand outstrips supply, prices go up.

When interest rates are low, people can borrow more money for the things they want. They can afford more expensive houses and vehicles. Easier to take out loans to do things like home improvement projects or buy boats and other recreational toys. Businesses can borrow money cheaply for projects or expansions.

Raising interest rates makes money more expensive to borrow, so people and businesses tend to borrow less. So less cheap money flying around reduces demand, which in turn should reduce prices.

The economy is essentially measured by transaction volume. Higher interest rates discourage transactions, while lower encourages. The more an economy spends (particularly in the private sector), the more opportunities arise, more goods become available, prices become fair and transparent, etc.

In an ideal state, there should be a natural equilibrium in the rate between borrowing and saving to keep spending more steady. Fed intervention signals a lack of equilibrium. Per your OP, to he change in interest rate has directly affected your spending behavior, you will not spend money on the your refi or buy a business. The bank now has less money to lend, and the seller of that business does not have the cash you would have otherwise given him to make another investment.

Further, increased transaction volume makes markets more efficient. If a buyer of raw goods has steady orders, competition develops on the supply side. The availability of more supply encourages competition on the demand/production side. The increase in competition on both supply/demand sides is good for the end consumer, as they should be able to find not only fair priced goods, but available substitutes. Thus, they purchase more and the upstream engine keeps revving.

Lastly, and I believe most importantly, volume of transactions creates tax revenue. If one wants to buy a good, they must earn enough income to do so, which of course is taxed. When they buy that good, they are taxed on the purchase and the seller taxed on the revenue. The seller buys more goods, they are taxed on the purchase, the seller on the sale, the shippers pay tax/tariffs on freight, etc. Obviously, taxes are primarily driven by transactions, not on tax rates; don’t let any idiot tell you the trickle down economy is not real, it’s science. Unfortunately, we (our politicians) have built this house of cards that our economy is very dependent on public spending, which has been made possible by low interest rates. If transaction volume decreases (lower rates), tax revenue will decrease, in order to sustain these public spending programs, even more will have to be funded by borrowing, which will now be more expensive due to interest charges. In other words, our economy has been propped up artificially by government spending that has increased to levels not possible to sustain in a high inflation/rate environment.

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How does raising Interest rates reign in already High inflation on product goods? What should be the goal we(fed) want to achieve here? What should we expect?

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Personally, I was going to refi in 2023. Not happening now.(Due to rates)
Was going to look at buying a small business. On hold now.(Due to rates)

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You answered your own question.

Yes, and I understand that goal by the Fed. I'm just trying to figure out in my tiny little brain how taking money out of circulation helps lower the Inflation problem.

Very quickly - Higher interest rates temper demand and when demand decreases price usually goes down overall. It may not do much to supply given the already present supply constraints but may have an impact.

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1) How does raising Interest rates reign in already High inflation on product goods?

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TL;DR - As others have said, raising rates means less borrowing and more saving (by both businesses and consumers) as it becomes more expensive to borrow money.

Longer version:

The US Dollar (USD) is a fiat currency, that is a currency whose value isn't tied directly to the price of something else (like an ounce of gold, for example). This means that the more USDs there are in circulation, the less value each has.

One of the ways the Fed injects money into the economy is by loaning money to banks (the other is buying US debt, aka securities). Banks have to keep a certain amount of money available at all times (their reserve), so if there is more demand than they can meet without dipping into their reserves, they borrow from the Fed. They factor in how much the Fed is charging them into the loan they are making to you or I (or our businesses). As the Fed raises the rate they charge banks, banks also raise rates on what they charge you and I (but not always at a 1:1 ratio).

By keeping rates extremely low for so long they've devalued the Dollar (the taking of more Dollars to buy the same item due to the value of the Dollar going down is "inflation").

The following is paraphrased from an example I once heard given by the late, great Dr. Walter E. Williams.

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Let’s say you’re walking down an old dirt road and you’re starving. I don’t mean “I missed my mid-morning snack and am simply faaaaaamished”. That’s merely “hungry”. I’m talking about “I haven’t had a single morsel of food in over a week and my organs might begin shutting down on me soon”. I mean starving.

As you do your best to ignore that ever-present gnawing in your stomach, in the distance you notice a sign on the road. As you get closer you see that it’s advertising “24-HOUR ALL YOU CAN EAT BURGER BUFFET – ONLY $1.00!” and beyond that you see the restaurant in the distance.

You begin to feel hope, but then quickly remember that you are flat broke. You don’t have a dollar, you don’t have even a penny.

You become even more dispirited.

As you continue to trudge along the road, contemplating your eventual death from starvation, you see a crumbled, dirty dollar bill on the side of the road.

In that moment, how valuable to you is that dollar bill? Pretty freaking important, I would guess. That crusty old dollar literally means you get to continue living.

Now, imagine that entire exact scenario except that instead of being broke you’re pulling a wagon filled with dollar bills all stacked and bound but easily accessible. How valuable to you is that dirty, crumpled roadside dollar now? Would you even bother to pick it up?

That difference in attitudes towards that roadside dollar is the inflationary effect of too much money in an economy.

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So by raising the rates, the Fed is essentially removing Dollars from that wagon you're pulling, thus making each remaining Dollar worth more... eventually.

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What should be the goal we(fed) want to achieve here? What should we expect?

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The Fed has stated their goal is to have their target range at 3%-4% by the end of the year (currently it's at 2.25%-2.5% LINK). If they stick to their goal then we can expect another .5%-1.75% in increases before the end of the year (they have two more meetings this year, Sept and Nov, in which to do this).

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I'm just trying to figure out in my tiny little brain how taking money out of circulation helps lower the Inflation problem.

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With less money in circulation Santa can no longer pay these high prices for materials for his elves to make toys. Since Santa won't pay the high prices the material suppliers have to charge less in order to sell their inventory

Now do the Tooth Fairy