Depending on the nature/origin of your data, a simple first way of detrending would be to use a log-linear model for your time-series.
For instance, for $Y$ the model would be
$log Y_t = y_t = \alpha + gt + \epsilon_t$.
where $\alpha+gt$ is your trend component and $\epsilon_t$ the cyclical component.
(Note that $t$ indexes time).
Below is an example with data from the FED.
If you would take log-differences ($\Delta y_t = y_t - y_{t-1}$) you get something equivalent to a growth rate with a constant trend growth $g$ and the change in the cyclical component ($\Delta \epsilon_t$).
Important caveat with this approach is that there might appear to be a mean-reverting cyclical component, which is not there.
Instead you could also use a Hodrick-Prescott filter.
Depending on the software you use there is also decompose in R which can help remove the trend and seasonal component.
I am sure others can add more useful suggestions as well.
Example GDP data US.
library(Quandl)
gdp <- Quandl("FRED/GDPC1",order="asc") #data
gdp <- ts(gdp$Value,start=c(1947,1),frequency=4) #time-series: quarterly
gdp<-log(gdp) #log-transform
gdp.dt<-ts(residuals(lm(gdp~index(gdp))), start=c(1947,1),frequency=4) #detrend
plot(gdp.dt)
