How to use SQL find first matching result from one table in another table?

Question

Suppose I had two tables:

Customer -
ID  | Name  | Etc
1   | One   |
2   | Two   |
3   | Three |
4   | Four  |
5   | Five  |
... | ...   |

Sales - 
Customer ID | Date | Amount
5           | 1/20 | $45
5           | 3/19 | $145
3           | 8/19 | $453
7           | 3/20 | $4513
3           | 9/20 | ...
1           | 3/20 | ...
1           | 1/20 | ...

What I want to do is write a query that will find the first sale for each customer. I am not sure exactly how to do it. I feel like this is group by problem, but the answer is not coming to me.

EDIT: I feel like my first data table did not fully explain my problem. (Honestly, I didn't even realize this facet of my problem until, I was coding the solution) Note: There is more than one customer per sale.

Sales - 
Sale ID | Customer ID | Date | Amount
1       | 5           | 1/20 | $45
5       | 5           | 3/19 | $145
8       | 3           | 8/19 | $453
7       | 7           | 3/20 | $4513
3       | 4           | 9/20 | ...
2       | 1           | 3/20 | ...
1       | 1           | 1/20 | ...

Answer 1

You can use a subquery which assigns a row number to each sale for each customer, ordering by ascending date, and then select only the first rows:

SELECT "Customer ID", "Date", "Amount"
FROM (
  SELECT "Customer ID", "Date", "Amount",
         ROW_NUMBER() OVER (PARTITION BY "Customer ID" ORDER BY "Date") AS rn
  FROM Sales) s
WHERE rn = 1

Demo on SQLFiddle

Answer 2

Nick's solution is probably the most performant, but if you wanted to use GROUP BY here, you could do that:

SELECT
    c.ID,
    c.Name,
    s1.Date,
    s1.Amount
FROM Customer c
INNER JOIN Sales s1 ON c.ID = s1."Customer ID"
INNER JOIN
(
    SELECT "Customer ID", MIN(Date) AS FirstSaleDate
    FROM Sales
    GROUP BY "Customer ID"
) s2
    ON s1."Customer ID" = s2."Customer ID" AND
       s1.Date = s2.FirstSaleDate
ORDER BY
    c.ID,
    c.Name;

Answer 3

In Oracle, you can use keep :

select customer_id, min(date) as first_sales_date,
       max(amount) keep (dense_rank first order by date asc) as first_amount
from sales
group by customer_id;