As you may be aware, the matchmaking system in Dark Souls 2 is completely different to that of Dark Souls 1. In Dark Souls 1, your Soul Level determined who you could summon and invade, whereas in Dark Souls 2 it is based entirely on your Soul Memory, which is the total number of souls you have collected with that character. They also differ in another important way: the Soul Level range was based on percentages (specifically +/- [10 + 10%] of your own), but Soul Memory is instead divided up into many tiers, and then the range is a certain number of tiers above or below your own.
This has the implication that there is no reason to stop levelling, as you will continue to go up in tiers anyway and get matched with tougher opponents in PvP or challenges in Co-op. However, some community members like to stop at Soul Level 120 or 150 as it promotes using builds rather than being able to do everything with one character, thus making PvP more interesting. This of course means they will have to organise specific events or fight through higher level opponents in order to face other players who also capped their level. On the other hand, there is no shortage of end-game PvP for players who want to continue levelling up.
Another downside to this system is that it is no longer possible to design a character for jolly co-operation at a particular boss, because eventually the souls gained by beating the boss as a phantom will push your character out of the typical Soul Memory tiers of players facing that boss.
While some view the new system as negative progress, presumably the intent was to prevent the prevalence of "twinks" from Dark Souls 1, where players could play through the whole game at a low level and get end-game equipment and upgrades to weapons then return to early areas and completely outclass new players they invade.
Anyway, the rest of this guide will detail the tiers and how each multiplayer item uses them.
White Sign Soapstone
White Sign Soapstone with Name-Engraved Ring
Small White Sign Soapstone
Small White Sign Soapstone with Name-Engraved Ring
Red Sign Soapstone
Cracked Red Eye Orb
Cracked Blue Eye Orb
Crest of the Rat
Bell Keeper's Seal
Ranges for the Guardian's Seal and Crest of the Rat haven't been retested for the latest patch yet. The new range is likely slightly larger than what is currently listed.
Step by Step
Find your Soul Memory. This is the number in the top right of the Player Status screen.
Find which tier you are in. Look at the table above and find the row where your Soul Memory fits between the lower and upper bounds.
Find the range for which item you are using.
Go down and up the tiers based on the range of the item. The lower bound of the lowest tier and the upper bound of the highest tier are the full range of players available to you.
My soul memory is 680,000.
I'm in tier 21 (600,000-699,999).
I'm using the White Sign Soapstone, which goes down 2 tiers and up 1.
The range is then from tier 19 (450,000-499,999) to 22 (700,000-799,999), so the full range of players who can summon me is 450,000-799,999.
In general, you can't connect between NG and NG+ at all. However, NG+, NG++, and so on can connect to each other. Since the SotFS patch, there are no restrictions based on playthrough.
You can only see White Sign Soapstone summon signs when human and there is still a boss alive in the area you are in. Small White Sign Soapstone summon signs will show up even after the boss is dead.
Being in the Heirs of the Sun Covenant doesn't increase the SM range, it simply makes your phantom/shade and sign appear golden. Whether it increases the chance of your sign appearing is unconfirmed.
The Name-Engraved Ring only seems to expand the SM range for co-op summons, but the filtering effect works with the Red Sign Soapstone and Dragon Eye too.
You can't summon or invade in Grave of Saints and Doors of Pharros, these areas are exclusively for Rat King Covenant PvP.
You can only summon one phantom or shade in Belfry Luna and Belfry Sol, presumably to prevent you ganking with 3v2 fights.
The Blue Sentinels arena has no restriction on Soul Memory.
Whether the Brotherhood of Blood arena has restrictions is currently unknown.
Abyss invasions are unconfirmed, but you can assume they work the same as regular Cracked Red Eye Orbs for now.
Mirror Squire invasions (coming out of the Looking Glass Knight's shield in NG+ and above) seem to ignore the NG/NG+ divide, although this is unconfirmed. Otherwise you can assume they work the same as the regular Red Sign Soapstone.
Also check out the relevant wiki pages for further information on matchmaking.
So Bandai Namco have posted some patch notes[bandainamcous.tumblr.com] for the changes in the upcoming Scholar of the First Sin patch early. There is quite a bit relevant to matchmaking, so I'll list the important points here. Note that these aren't guaranteed to be accurate and could change before release (February 4th-ish).
Players will gain access to a new item: The Agape Ring. When players equip the new Agape Ring, souls collected from kills during online play will be absorbed by the ring rather than the player. This allows players to control their online matchmaking experience by limiting their total souls collected. The Agape Ring absorbs the souls earned by the player, thus avoiding Soul Memory from increasing at the cost of a ring slot. Like the Name-Engraved Ring, this will likely be available from Sweet Shalquoir for a modest price at the very start of the game. This is most likely aimed at co-op, letting you stay at a particular SM and help players at a particular boss indefinitely. Unfortunately it doesn't quite seem to fix invasions and arena duels as orbs cost souls to buy.
The bonfire warp selection screen will now highlight the top three areas where players will have the best change to connect with other players online.
White phantoms will remain in other players’ worlds for longer periods of time. It was possible for some areas to cause the White Phantom to fulfil their duty before they reached the boss, such as No-man's Wharf; this is likely a bandaid solution for that. Presumably White Shades are not affected.
White phantoms will no longer return to their world if time runs out during a boss battle.
Players on their first play through can now match with players on their 2nd or further play through. i.e. removed the divide between NG and NG+, which means more possible matches.
Made it easier for players to match online in general.
Made it so that invading players cannot use items which invite more enemies. I'm assuming this means baiting an army of enemies to the host with Alluring Skulls.
Players may now choose to cancel out the effect of the Human Effigy at bonfires. New players would accidentally burn a Human Effigy instead of using it, having the opposite effect to that intended. Now that can be undone instantly instead of having to wait it off.
When a player cannot take part in online play due to the effect of the Human Effigy, made it so that the player can still write signs. (They still cannot summon during this period.) Burning Human Effigies now just prevents summoning and being invaded, but still allows helping others.
To prevent invasion after defeating area bosses, made the Human Effigy effect function in this situation automatically. No more invasions after the bosses in an area are killed. :(
There are also numerous adjustments to rewards for PvP, see the patch notes for details. In particular, Blue Sentinels and Brotherhood of Blood invaders gain more points towards their covenant ranks for successful kills, and Bell Keeper fights can reward a Twinkling Titanite, Petrified Dragon Bone or Titanite Slab instead of a Titanite Chunk.
Dark Souls 2 Soul Memory Visualiser[jakebarnes.com.au] by DuBistKomisch (me, shameless plug I know) - visualise the ranges for each item for any soul memory amount Dark Souls 2 SM Calculator[jpdesign.pcriot.com] by PySnow - gives the ranges for your soul memory, and can use another player's to check which items will work (seems like the website has gone down permanently)
This information is only known because of the hard work of illusorywall and their testing partners: optic_niko, hellkite_drake, ein death, hiroki sugihara, greensvadhisthana, and eur0pa.