Adding time to POSIXct object in R

POSIXct objects are a measure of seconds from an origin, usually the UNIX epoch (1st Jan 1970). Just add the requisite number of seconds to the object:

x <- Sys.time()
x
[1] "2012-08-12 13:33:13 BST"
x + 3*60*60 # add 3 hours
[1] "2012-08-12 16:33:13 BST"

The lubridate package also implements this nicely with convenience functions hours, minutes, etc.

x = Sys.time()
library(lubridate)
x + hours(3) # add 3 hours

James and Gregor's answers are great, but they handle daylight saving differently. Here's an elaboration of them.

# Start with d1 set to 12AM on March 3rd, 2019 in U.S. Central time, two hours before daylight saving
d1 <- as.POSIXct("2019-03-10 00:00:00", tz = "America/Chicago")
print(d1)  # "2019-03-10 CST"

# Daylight saving begins @ 2AM. See how a sequence of hours works. (Basically it skips the time between 2AM and 3AM)
seq.POSIXt(from = d1, by = "hour", length.out = 4)
# "2019-03-10 00:00:00 CST" "2019-03-10 01:00:00 CST" "2019-03-10 03:00:00 CDT" "2019-03-10 04:00:00 CDT"

# Now let's add 24 hours to d1 by adding 86400 seconds to it.
d1 + 24*60*60  # "2019-03-11 01:00:00 CDT"

# Next we add 24 hours to d1 via lubridate seconds/hours/days
d1 + lubridate::seconds(24*60*60)  # "2019-03-11 CDT" (i.e. 2019-03-11 00:00:00 CDT)
d1 + lubridate::hours(24)          # "2019-03-11 CDT" (i.e. 2019-03-11 00:00:00 CDT)
d1 + lubridate::days(1)            # "2019-03-11 CDT" (i.e. 2019-03-11 00:00:00 CDT)

So, either answer is correct depending on what you want. Of course, if you're using UTC or some other timezone that doesn't observe daylight saving, these two methods should be the same.