You are right, the esiest way is to reshape your data into a long format, see this example
library(tidyverse)
# Sample data on a copy/paste friendly format
dogfish <- data.frame(
YEAR = c(2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009),
QUOTA = c(4, 4, 4, 4, 4, 4, 4, 4, 4, 12),
LANDINGS = c(8, 4.9, 4.7, 3, 1.5, 2.5, 6.3, 6.4, 9, 11.7)
)
dogfish %>%
gather(type, value, -YEAR) %>%
ggplot(aes(x = YEAR, y = value, color = type)) +
geom_line() +
labs (x = "Year", y = "Millions of Pounds", color = "Legend") +
theme(panel.background = element_blank())

Created on 2020-09-29 by the reprex package (v0.3.0)