We have made both grass silage and corn silage.
The grass stuff we just raked up after mowing the lawn. We let it get a bit taller than normal before mowing. I wanted to just pack it into 5 gallon buckets with lids but the wife decided to use smaller trash bags to line the buckets. We let the clippings sit on the lawn overnight and raked them up the next day. Raked them up and packed them into the lined buckets. Twisted the bag shut and taped it closed and put the lid on.
It worked OK but the grass was a bit dry. We tried our experiment late in the year and I should have put the stuff up the same day. Earlier in the year the overnight wait might have been OK.
For corn silage we used to put up the leftovers from the garden with a chipper/shredder and that worked OK but was a pain to work with, it was slow and all the stuff was blown down near the ground so we were always stooping over. I bought a chopper body and the last time we did 1/8 acre of corn just for silage it went pretty quick.
Once the corn is chopped I pack it into old feed bags, pack pound stomp to get as much in as I can. Then I put the full bag into a trash bag and suck the air out with an old vacuum cleaner. I use the feed bags because they are a bit tougher than the trash bags and won't puncture but they aren't air tight so they go inside trash bags. Twist the bag and tape shut. This takes pretty much all the air out and that promotes the proper fermentation, exposure to air will wreck silage.
You could use 55 gallon drums with reusable lids if you have them and build some sort of lever with a packer attached. I thought about it but up here it gets pretty cold and moist silage may freeze in the barrel and then I wouldn't be able to feed it.
Storage is critical we lost a lot of the corn silage to mice and rates who dug through the plastic bags. In the future I will probably store them up on a hay wagon to try to get away from that.
Here is the rig...you can see the old chipper/shredder on the left. We aim the chopper into a plastic pallet with sides then fork out of there.
http://sefsufficient.com/drill/chopper1.JPG