This is a slight spoiler but the odds are, if you are here, you're looking for exactly this information. Basically, Preston Garvey is someone who will give you random quests to help settlers, and instead of asking you if you want to help, he will force each new quest upon you any time you turn in a completed one, or walk remotely near him. He seriously will not stop, ever. Via suggestions around the 'nets and some trial and error, I've worked out the sequence to successfully turning in Preston's missions while avoiding new ones.
1. Walk up to Preston and talk to him to start turning in the quest. He'll say a random thank-you/grats line or two.

Trouble Brewin' is a side quest in Fallout 4. The quest is received either by speaking to Rufus Rubins in Goodneighbor's Hotel Rexford, or from independently finding Buddy at the Shamrock Taphouse and interacting with him. When asking Rufus for work, he will ask the Sole Survivor to retrieve the Drinkin' Buddy, a protectron modified to function as a microbrewing machine, from the Shamrock. PC users are able to use Fallout 4's console commands to reset the affected quests via codes, so if you're having troubles be sure to scan the forum posts. The bug seems to be pretty huge and has.

2. Stay in front of Preston for the moment. He will now say something along the lines of 'I have a new mission for you.' Let him say this first line, otherwise the turn-in XP doesn't seem to pop properly in the next step.
3. As Preston is beginning to speak the first few words of the actual mission, walk/run away from him slightly and bring up your Pip-boy the moment you see the XP reward for the quest you just turned in. (If you stay standing there staring at Preston, the Pip-boy seems unresponsive. To be safe, you want to at least stay within earshot for this step or the turn-in XP may not pop.)
4. Fast-travel to somewhere else (Red Rocket Truck Stop will do).
5. Wait a few moments to make sure the new mission didn't register. Bask in the glow of the quest reward XP.

Fallout 4 Complete Quest Code

6. Done! :D
I managed to do this for two quests in a row, fast-traveling to Red Rocket Truck Stop both times without the new quest registering. Eat my shorts, Preston!
Update: It appears even if you never hear about the quests, you can fail them, which is stupid and has to be one of the worst game design decisions ever made. I've read elsewhere that failing those quests results in a permanent happiness loss at the related settlement, but I can't confirm this yet (I will at some point because screw Preston and his stupid quests). Every other faction I've come across with repeatable quests asks first you if you want to do them. And of course, it doesn't matter how ridiculously-fortified each settlement is, someone will always get kidnapped or think raiders can get through missile turrets and guards armed to the teeth. Stupid. Seriously, devs... what were you thinking? I'd shoot Preston between the eyes myself at this point, but he's immortal due to being a companion choice.
Update 2: Regarding the previous update, failing quests you never got in the first place may be glitched to not actually matter. I noticed that quests marked as failed for this reason seemed to reset if I went and talked to Preston out of curiosity. He gave me the failed quests all over again as if they were brand new (same location and everything) and didn't whine at me for having failed anything.
Also, if you avoid enough of the initial questline that leads to Preston becoming an active part of the ongoing game (hint: don't turn in the quest after you get the goodies on the roof of the building he's in), it appears that the random quests still do exist. I left Preston and friends where they are originally located with just enough of the quest left to make them stay there indefinitely, but later on discovered that a guard at Sanctuary (which I had populated via a radio beacon) had one of the usual 'omg someone has been kidnapped/whatever' quests. I reloaded a quicksave and avoided her from then on. The game has yet to tell me I've failed any such quests at any of the settlements that character is running, and that character has a lot of time in-game after the initial meeting with Miss Quest Guard Of Doom.This is a slight spoiler but the odds are, if you are here, you're looking for exactly this information. Basically, Preston Garvey is someone who will give you random quests to help settlers, and instead of asking you if you want to help, he will force each new quest upon you any time you turn in a completed one, or walk remotely near him. He seriously will not stop, ever. Via suggestions around the 'nets and some trial and error, I've worked out the sequence to successfully turning in Preston's missions while avoiding new ones.
1. Walk up to Preston and talk to him to start turning in the quest. He'll say a random thank-you/grats line or two.
2. Stay in front of Preston for the moment. He will now say something along the lines of 'I have a new mission for you.' Let him say this first line, otherwise the turn-in XP doesn't seem to pop properly in the next step.
3. As Preston is beginning to speak the first few words of the actual mission, walk/run away from him slightly and bring up your Pip-boy the moment you see the XP reward for the quest you just turned in. (If you stay standing there staring at Preston, the Pip-boy seems unresponsive. To be safe, you want to at least stay within earshot for this step or the turn-in XP may not pop.)
4. Fast-travel to somewhere else (Red Rocket Truck Stop will do).
5. Wait a few moments to make sure the new mission didn't register. Bask in the glow of the quest reward XP.
6. Done! :D
I managed to do this for two quests in a row, fast-traveling to Red Rocket Truck Stop both times without the new quest registering. Eat my shorts, Preston!
Update: It appears even if you never hear about the quests, you can fail them, which is stupid and has to be one of the worst game design decisions ever made. I've read elsewhere that failing those quests results in a permanent happiness loss at the related settlement, but I can't confirm this yet (I will at some point because screw Preston and his stupid quests). Every other faction I've come across with repeatable quests asks first you if you want to do them. And of course, it doesn't matter how ridiculously-fortified each settlement is, someone will always get kidnapped or think raiders can get through missile turrets and guards armed to the teeth. Stupid. Seriously, devs... what were you thinking? I'd shoot Preston between the eyes myself at this point, but he's immortal due to being a companion choice.
Update 2: Regarding the previous update, failing quests you never got in the first place may be glitched to not actually matter. I noticed that quests marked as failed for this reason seemed to reset if I went and talked to Preston out of curiosity. He gave me the failed quests all over again as if they were brand new (same location and everything) and didn't whine at me for having failed anything.

How To Reset A Quest In Fallout 4 Walkthrough

How To Reset A Quest In Fallout 4 Ps3

Also, if you avoid enough of the initial questline that leads to Preston becoming an active part of the ongoing game (hint: don't turn in the quest after you get the goodies on the roof of the building he's in), it appears that the random quests still do exist. I left Preston and friends where they are originally located with just enough of the quest left to make them stay there indefinitely, but later on discovered that a guard at Sanctuary (which I had populated via a radio beacon) had one of the usual 'omg someone has been kidnapped/whatever' quests. I reloaded a quicksave and avoided her from then on. The game has yet to tell me I've failed any such quests at any of the settlements that character is running, and that character has a lot of time in-game after the initial meeting with Miss Quest Guard Of Doom.