This is very long...I ran out of typing ability since I do this with two fingers. There will inevitably be mistakes in spelling, missed words, and poor sentence structure. There's also the likelihood I put some steps out of order or missed entirely.
Lets speak generically. There's a lot of adjustment that need to be pretty close to right for a sickle to work to work good. The first thing to do is buy the owners manual someplace, it will have almost everything you'll need in it to make all the required adjustments. But until you get one there's some common sense things you can do. Since the mower is new to you remove the knife bar and make certain it's absolutely straight. That shouldn't be too hard.
The sections are likely riveted on, if they are in excellent shape just leave them but if they are dull, chipped or broken then replace them and use bolts (some call them screws) and nuts designed for the type of section you are using. My limited experience with various machines all used the generic bolts. If you have long workbench it makes it much easier, I use my hay rack deck and some cut 2x4's to hold the bar up to drive the rivets out after grinding the heads off. They make tools for removing and re-riveting riveted sections and they make a tool for installing bolts too. I modified my rivet tool to work with bolts. Don't try to pull a bolt in with the nut... it might lead to disappointment.
Now, before the knife goes back in inspect the wear plates (if it uses them), they should be under a few of the guards but not all of them. If it has them they are likely worn down. Those are inexpensive so set them in where they came out use good judgement, they can be put under every guard but that just adds friction and heat, too few and the knife flexes too much. My personal choice is every third guard across the center and one on each end regardless of where the nearest one is. Just inspect them at this point, don't remove them.
Put the knife back in the bar and working off the wobble box. Now you need to check register. That is when the individual section tips are centered perfectly in the guard at both ends of it's travel. That's a function of moving the drive box (wobble box) one way or the other, be prepared...the bolts and/or nuts to hold this are very tight! That box is under a lot of stress. Look for at least four and more likely six or more bolts holding the box in place. It should be able to move sideways to center the sections at full throw on both ends of the travel. If they are fine leave that alone. Close works but they have to be close.
Next up... multiple items. The guards, wear plates (mentioned above if any are used) and hold downs are likely attached with the guard bolts. Replace the wear items at this time. Replace them all at once to save labor later. Mount them loosely in this order... wear plate on the bar (it needs to be clean and free of rust), guard, hold down on top. But this depends on the type of guards used one piece or two piece. I won't go into the two piece guards because I've never seen them.
OK, now the knife is a razor blade so keep close watch on all your fingers. It should move freely in the guards at this point. The sections should be centered in a guard. The wear plates should be installed (as well as new guards if the ledger is rounded bad) and good hold downs too (BTW, bolts holding the sections on might require high guards, rivets won't) so now the knife can be set snug with the wear plates (or whatever the 30A uses for to do that). This is done by pushing the knife forward into the guards until the underside of the spine of the knife is snug to the inside wear area of the guard. On all the sickles I've owned the wear plates do this. It's frustrating getting them all the same. Just don't get them too tight. The knife always has to move freely or with just the slightest amount of resistance. At this point it might be a good idea to remove the knife from the wobble box again.
Nobody said these old sickles didn't require a considerable amount of time getting correct. But once they are correct keeping them that way is easier. And a correctly working sickle will cut beautifully, quietly, and leave a lawn smooth stubble.
Back to adjusting... now the knife is snug (not tight) to the front of the guards knife spine recess, all the fore and aft adjusting is done as equally as possible between all the parts, tighten all the guards down. Check and make the adjustment parts haven't moved. If all is good on to the next adjustment.
Grab some strong string or use your eyes (eyes can play tricks, string won't). Stretch the string between the farthest guard teeth on each end and as far towards the point as you can get it. Construction (braided) line works best because it can be piano wire tight. The objective is to line up the tips of the guards all across the bar in a perfectly straight line. This will put all the ledgers at the correct height relative one another. It's another frustrating part. There's some nuances here. Getting the tips lined up relative to the bottom of the bar will will reduce the draft on the bar as it's cutting. More on that later.
I put a straight edge under the bar facing forward and set the first guard the string is attached to at the middle of the thickness of the bar. I found that's a good compromise because I could never find an official measurement for that, Just using your eyes for that works too. Just don'tpoint the the tips of the too much up or down in relation to the bottom of the bar flat. Now set all the tips of each guard as close to the string as is humanly possible. A good heavy piece of pipe slipped over the tip to use as leverage to bend the tips or down works good (disclaimer- all the guards I have used are malleable iron, check yours first before trying to bend them) Some older guards I understand where made of cat iron, try and bend those and you'll be buying a new guard.
OK, now all the tips are in line. Now on to the hold down adjustment (for me this is day two). There's a LOT of tightening, loosening, tightening, readjusting, etc.in all those previous steps.
The hold downs I'm familiar with can't be adjusted readily while they are on the machine. Everyone (and my owners manual) says they can be....I've never had such good luck. YMMV. The hold downs I use are the generic John Deere type. I'm not familiar with any other kind. The principles are the same however. The knife sections need to be within a couple of thousandth's of the ledgers. Tight on the ledgers is not good, too much friction. But the section will move away from the ledger a very small amount so keep them as tight as possible without rubbing. Some wisdom says that hitting the top of the hold down sharply with a mallet will move the guard away from the section, and hitting the front edge will move it closer. There's only two problems I've found with that; the sections are in the way in both directions. The guard has now room to move past it's memory position from the top and the sections are in the way from the front so the risk of damaging them is significant. It's better to get them pretty tight by removing them one by one and bending them in a vise by clamping onto the mounting hole side. Then use a flat ended punch from below to move it up so it just keeps the section snug on the ledger.
Now oil everything on the bar, make sure the sickle moves still moves freely, attach it firmly and correctly to the wobble box, hook it the PTO shaft to the tractor and start it up and run it slow, listen. If everything was done correctly it should has a whisper quiet sound coming from the cutters. A swish, swish swish sound. It should shave one inch of grass off a lawn with ease.
However, all that hard work and frustration won't last long in a field of tall grass with woody weeds. Woody weeds are timber weeds (otherwise known as giant ragweed) thistle, burdock, and a plethora of other woody weeds. But with everything near to perfect now it will take much less time to get it back that way at the end or start of the next season.