Step 1.) Remove the pressure plate inside the back door of your Trip 35, it's quite easy to slide out, just don't force it.
Step 2.) Look at the number printed here:
The first, Japanese, symbol is the factory code and is not so important. The 9 is for the year, and the 3 for the month. The earlier Trips have a chrome shutter button, and some time in the mid 70's the shutter button was changed to black. Mine has a chrome shutter button and so was manufactured in March 1969, which is confirmed by my low serial number. If it had a black button it would have been manufactured in 1979. They were only manufactured between 1967 and 1984, so there shouldn't be any problems placing the year of manufacture depending upon the colour of the shutter button. Easy, huh?
Step 3.) Put your pressure plate back into your Trip, carefully.
Step 4.) Put in some film and go shoot something!
PS: If you have a refurbished Olympus Trip 35 then this may not be completely accurate because the companies that do the restorations freely swop parts between cameras as spares are needed.