There are two versions of SQ4 around. The first is the original diskette version and the second is the enhanced CDROM version which includes narration instead of text as well as some other extra audio. The game play is the same except that the diskette version includes copy protection quite early in the game. The CDROM version was available as a separate CD and is also the version that is included in the 15th Anniversary Space Quest Collection CD.
I've split it up into sections to which you can jump if you want to:
Make your way to the right and pick up the rope that is near the bottom of the screen to the right . Then make your way back left to the screen you started on and left again, where you will see a wrecked hover-car. Look inside it and open the glovebox. Take out the PocketPal laptop . Close the glove-box again if you have a sense of neatness, otherwise don't worry about it. Make your way up the screen to the middle left screen. Look in the hole in the tank and take the unstable ordinance . Use your better judgement and put it back .
Make your way up again, into the upper left corner. Hide behind the bank's pillars and lay the rope out on the ground. Wait for the cute little pink bunny to come hopping along. When it hops into your noose, pull on the rope . Take the power cell out of the bunny  and put it into the laptop . You get points for successfully hiding from the flying robot. So find somewhere to hide, for example under the overhanging roof at the right of the top right screen or under the big pipes at the right of the bottom right screen. After quite a while the robot will come, it won't be able to see you and will leave .
Then make your way down to the middle right screen. Open the topmost grating and hop in . Take the bottle into custody  and press the button that's under the blotter on the table . Listen to the message, then open the sewer hatch and enter the sewer. The easiest way to the other side is just up a bit, then left all the way to the other side then down to the ladder. Some green slime will come out of a grating and follow you. Scoop some of the slime up in the bottle  and then leave and climb up the ladder before the slime decides to scoop _you_ up.
When you open the hatch into the street, you'll see a Sequel Police patrol ship land. When the Sequel Police have left the ship, get out of the manhole  and make you way to the ship. Get in the landing gear hatch  (the grey bit near the bottom centre of the orange ship). (When I first played the game on my 386 I didn't have any trouble with this bit. When I played the CD version of the game on my Pentium the Space Police kept getting me. The Space Police get quicker, even if you put the game speed down. So you have to push the game speed up and make a run towards the ship as quickly as you can. You must click the hand icon on the hatch to get into it. If you still can't do it, try slowing your computer down with a slowdown program such as "mo'slo" or "turbo".) You'll get taken up to the headquarters. Go to the left, you will see a time pod appear. When the Sequel Policeman has left the pod, make a run for it and jump in . (If you're playing the original diskette version of the game you'll have to answer a copy protection question here. The Multimedia CD version doesn't have the copy protection bit.) Now you will be faced with a row of symbols on a screen; write these down because you'll need them to get back here later. Now you'll have to enter other symbols to get elsewhere. Try a few combinations of symbols and eventually it'll take you to Space Quest X. If you type in the whole top row in order and then the first symbol from the second row, you'll end up on Ortega in Space Quest III - but you'll die there so don't do it unless you've saved. :-)
Then get out of the hole in the bottom left of the nest, you'll fall into some water and get captured by some women. Zondra, who we assume Roger meets somewhere between Space Quest IV and Space Quest X, is ever so slightly peeved and drags you off to their fortress.
You'll be tied to a chair and Zondra will leave you at the mercy of Thoreen and her EpiRip 357. A giant sea slug will appear and scare the women off. When the slug reaches for you with its tentacles, it will accidentally open your restraints, allowing you to press the little red button near your right hand . This will zap the slug's tentacles with the same things that took your trouser legs off. Take this opportunity to grab an oxygen cylinder  which you throw into the slug's mouth when it grabs you again . The girls are ever so happy, Roger is forgiven his misdemeanors, and they decide to go off to the Galaxy Galleria to shop and celebrate.
Try to use the ATM and it won't work because you don't look like Zondra. Then go to Sacks and buy some women's clothing, it will cost you B$60 . Then go to the ATM near the Software shop and clean house . Go into the Software shop and buy the Space Quest IV Hint Book . Go and retrieve your clothes from the changing booth at Sacks .
Make your way to the Arcade. Have a game of Ms Astro Chicken if you want to. (No points attached though, unfortunately.) If you have done everything in the Galleria that you're supposed to have, the a Sequel Police time pod will appear. It's best to be standing on the right hand side of the arcade when this happens. Now you have to try to avoid the Sequel Police and get back to their time pod. This was quite simple for me the first time I played it. I did the following: Get out of the Arcade and go to the near entrance of the Skate-O-Rama. Float up into the top half of it (i.e. off the top of the screen on which you start). Stay near the left and wait for the Sequel Police to arrive from the right, then go back down into the bottom half and get back to the arcade.
When I replayed the CD version on a faster computer it was harder. I got it to work like this though: Go out of the arcade and go around to the other entrance of the Skate-O-Rama. You have to go around the back because the Sequel Police are waiting at the front where the entrance of the Galleria is. As with the bit where you get into the patrol bit in the beginning, you have to push the speed up and do this next bit as quickly as you can; you should probably save the game on the steps just outside the Skate-O-Rama so that you can keep trying it. As quickly as possible, jump into the Skate-O-Rama and float up to the top half. When you get there, go to the left half of the top and wait near the left hand side. Then when the Sequel Police appear from the right you can go down and back to the arcade. Once you've left the Skate-O-Rama you can slow the speed down again so that you can deal with the moving walkways more easily. As with getting into the Sequel Police ship near the beginning, if you still can't manage to do this, use a program to slow down your computer.
When you're back in the arcade get into the time pod . Write down the code that is currently on the screen. Put together the pieces of the codes from the gum wrapper and the hint book (the bit from the hint book coming first) and type it in .
Now would be a good idea to plug the connector that you bought into the PocketPal . Go into the computer. Plug the PocketPal into one of the connections if you want to, to see where you are , but be quick because there are a few nasty droids that will shoot at you if they see you. The place you want to go to is the place in the bottom left. Make your way there without being shot , type in the code from the hint book and enter the room .
You will be presented with a Windows-type interface. First flush the droid icon down the toilet  and the brain icon . This will start a timer, which means you should hurry for the rest of the game. Flush the other icons for fun if you want to. If you're going to flush the SQIV icon, save first. (The effect is great though.)
Next, make your way to the top level and to the top of the screen where you will enter a tunnel and emerge in Vohaul's chamber, which you will have seen before from the 'Meanwhile, back in Space Quest XII' bit . After a bit of dialogue, you'll have a fight with Vohaul who has inhabited Roger Junior's body. Push forward every now and then and try not to be killed. After a while you'll knock Vohaul back into the beam and he'll be suspended. Climb down the ladder and fetch the disk that Vohaul threw away .
Put the disk into the computer that is on the platform . Upload disk, upload beam, change the pointer on the right to point to Roger Jr, download beam [315/315]. Roger Jr is restored, Sludge Vohaul is defeated and everything ends happily, albeit a bit confusingly for poor Roger.