I know that most of the datasets from ATLAS or other particle physics experiments are terabytes, but I was just curious is there any place where one can find them to download? And one more question, which software they are using to analyze data and do the simulations? Plus if there is any guide available where they show setting up the software and analyzing some smaller particle physics datasets, I would be glad. I kept searching the Internet for similar things, but unfortunately couldn't find anything.
Geant4 is probably the closest thing you could conceivably get. It's a detector simulation software package with a steep learning curve that's heavily used in the HEP community, and, as far as I know, is available for anyone to download and build. Full disclosure - I did HEP experiment once upon a time but that was 20+ years ago. So if someone currently active corrects me on this point, I'll withdraw the answer - but I doubt if Geant4 would be useful to anyone without at least some training in HEP and detectors. Still, it would give you some sense of what you are up against.
One of the comments mentioned the Kaggle Higgs competition, as far as I know that's already heavily processed data, but in theory it's available to anyone.
I doubt if any collaboration would provide raw data from experiments publicly without some verification that the person requesting it knew what they were doing.
Cautionary note- HEP data analysis isn't like amateur astronomy - it takes a large team. Just look at the length of the author list on any typical HEP paper.
If you are just looking to simulate the data produced at the LHC then the right program to use is Madgraph. It is by far the most popular Monte Carlo generator to use for simulations at the LHC and can produce events for any process you want. Madgraph will then also invoke Pythia and PGS to simulate hadronization and detector simulations if you wish. There are many built in models that you can use for your simulations (SM, MSSM, etc.) and you can also write your own, though that has a steeper learning curve. There are many tutorials online that you can follow to get it working on your machine.
If you are looking for actual data then I believe you have to go the papers published by CMS and ATLAS they often publish tables that you can get the data from.
All of the existing answers to this question are now out of date, because CERN has released data for all of its experiments through its Open Data program, including data taken as recently as 2016. There is sufficient data to, e.g. discover the Higgs boson for yourself, along with ample documentation.
Whenever searching for datasets, I always look at Kaggle, Google Dataset Search, and the Ultimate Dataset Aggregator. From doing a quick search, there doesn't seem to be a lot out there. However, recently there has been a resource uploaded to Google Dataset search (screenshot below) from the California Institute of Technology and CERN. This may be worth a look.