Hello! I just got MHP3rd HD and I thought I would post a few helpful tips as I figure out how to get things working.
IMPORTING YOUR SAVE
Once you install the game on your PS3 you will will to import your save from your PSP. This is done by connecting your PSP up to your PS3 with a USB cord. Make sure your PSP is in "USB Mode" the go to your PS3 and under the "Game" tab you will see a Save Data Uility file labeled PSP Remastered/Minis/PSP (or something close to that) , find your MHP3rd save file in there and copy it. You can now disconnect your PSP from your PS3.
On your PS3 start your game, you can chose the first option to start playing single player. (I suggest doing this then climbing in your bed and saving, I don't have a reason why, it just felt like it confirmed everything for me, LOL.)
GETTING ON AD HOC PARTY
If you want to play on Ad Hoc Party make sure you have the Japanese version installed on you PS3, if you do not simply go to the MHP3rd HD game disc under the game tab on the XMB. DO NOT press x to start the game, instead chose the 2nd option and it will get ad hoc party installed for you. Once that is done quit it and start up MHP3rd. When it starts up chose the option on the right!
Then you will be on the japanses ad hoc screen. Before you begin you have to accept some terms or something, so make your way through those. (It took me a few tries cause I think I kept backing out or hitting x instead of o or choosing the right option when it should have been the left one, you'll get through with trial and error eventually) once that is done go to start and then select the world and room as you normally would then you can switch to the game once in a room by pressing, R2!!! And enjoy! It is awesome! ...well I think it is I haven't been able to actually play it yet.
Alright guys, I hope this at least helps get you started. Unfortunally I have got to get to work. I only had about 20 mins to figure things out so there may be kinks here and there. I will be back tonight to post any more info and help if there are questions. I do not know Japanese so I figured this out with just messing around. If we all just help eachother and post what we have figured out the language barrier should not be a problem. See you on Ad Hoc tonight!