In period, when close relatives (fathers, sons, brothers...) were all alive and kicking, they would do slight variations of a theme to show that, while they were related, they were not the same person. Typically, these devices were only one step away from each other, like having a field of a different color, or adding a chief. In some places and times, there were specific ways one was supposed to change their device based on how they were related to the current holder of the unchanged arms- a first son would add a label, for example.
In SCA armory, two differences are required to show that you make no claim of relation to the person bearing similar arms. You can, of course, ask for letters of permission to conflict (LoPtC) regardless of relationship, but when designing your armory, don't submit it if you know of a conflict and haven't received a LoPtC.
There were a series of conflict-checking classes at KWHSS. The one I went to was run by Pipa Sparkes, who supplied a very handy cheat sheet which I've been using extensively. To conflict check, you'll want to access the SCA armorial and/or ordinary (oanda.sca.org) and potentially the compiled precedents (http://heraldry.sca.org/laurel/precedents.html).
You'll also need to know how to read a blazon. The field comes first, followed by a comma. Then comes the primary, followed by any secondaries, tertiaries, peripherals, and lastly overall charges.
Azure, on a bend between two cups Or, an arrow azure
the field is azure, the bend is the primary charge, the cups are secondaries, and the arrow tertiary. In:
Sable, a gryphon passant within a bordure argent
the field is sable, the gryphon is the primary, and the bordure is the peripheral.
Argent, three bendlets azure and overall a cross moline gules
the field is argent, the bendlets are the primaries, and the cross is overall.
Sometimes there are no primaries, so in:
Or, a tierce gules.
the field is Or and the tierce is a peripheral.
So now that you know what your charge groups are, you're ready to do some conflict-checking.
Step 1: Identify the primary charge group.
A) Addition or removal of primary charges means no conflict.
A rose does not conflict with a lack of primary charges.
B) Substantially different primary charges on simple armory means no conflict.
Simple armory is armory with no more than two charge types which both lie directly on the field. In my previous post, the triskelion of legs is one type of charge while the bezants are another. There's nothing else on the device, so it's simple armory. The pall with an overall gryphon, however, is not simple armory because the overall charge does not lie solely on the field. Note that all charge types must be substantially different (a cross and a sword in bend can potentially conflict with two crosses in bend).
So look for armory that has the same type of charge(s) as your piece. A leopard's face does not conflict with a sword. If your piece has a wolf's head as the primary and someone else's has a dog's head, they can potentially conflict because there isn't much of a difference between a wolf and a dog as far as heraldry is concerned. Knowing what charges do and don't conflict is simply a matter of learning it through a mixture of common sense (a cat looks nothing like a shoe) and memorizing or looking through precedents (the SCA does not grant a difference between rampant and salient, for example).
If, via these two rules, nothing conflicts, then congratulations! Your device probably has no conflicts (Make sure to ignore "transparent charges" like laurel wreaths. I won't go into that right now.). Skip to Step 3. However, if you have a list of potential conflicts, you must now make sure none of them are less than two steps away from yours (In our jargon, these are called "clear differences", or CDs. However, this will probably change when the new rules go into effect, making it "distinct changes", or DCs.). So on to-
Step 2: Counting differences
Pipa did a fantastic job with her cheat sheet, so all but the italics is basically copied and pasted directly from it.
A) Field difference (i.e., my field is different; what does this mean for me?)
i) Charged fields (other than uncharged peripheral ordinary): all field changes=1 CD Max
ii) Field-primary armory has uncharged peripheral charges only: chief, bordure, base, canton, gyron, orle, flaunches...
(a) Substantial change of partition type= no conflict
(b) Complete change of tincture (including furs and field treatments) = no conflict
(c) Other field-primary armory: all other changes= 1 CD
iii) Fieldless vs. field/less, tinctures vs. no tinctures, & Japanese mon= 1 CD
B) Addition/removal of charges on field= 1 CD
C) Addition/removal of charges overall= 1 CD
D) Tincture changes (including furs) to charges on field= 1 CD
E) Type changes to charges on field= 1 CD
F) Number changes to charges on field (note that a semy can be anywhere from 6 to however many the person/heraldic artist cares to put on there)
i) 1, 2, or 3 vs. any other number- 1 CD
ii) 4 vs 6+= 1 CD
iii) 5 vs. 8+= 1 CD
iv) 6+ vs. 7+= no CD
G) Arrangement changes to charges on field (charges in fess vs. charges in pale)= 1 CD
H) Posture changes to charges on field (this is the attitude and only major changes count, i.e. rampant vs. passant as opposed to statant vs. statant reguardant)= 1 CD
I) Addition/removal of tertiary charges= 1 CD
J) Changes to tertiary charges
i) At least 2 changes to tertiary charges= 1 CD Max
ii) If all of the following are true= 1 CD Max
(a) 1-2 types of primary/secondary charges: (1) simple and void-able, and (2) correctly drawn with an interior substantial enough to display easily recognizable charges
(b) No overall charges
(c) Substantially changing the type of all charges of a tertiary group
If, at this point, you still have at least one potential conflict, either seek out an LoPtC from the holder of the armory or change your design to avoid conflict altogether. If you have successfully removed all of the potential conflicts via at least 2 CDs each, then you get to go on to the last and final test-
Step 3: Visual test
This one doesn't come up often because being two CDs clear usually makes pieces of armory look completely different, but on occasion devices which don't technically conflict still look a lot alike and will be counted as a visual conflict. For example:
The submitted device:
Per fess azure and argent, a pale counterchanged
The registered armory:
Party of six azure and argent
A party of six means the field is divided per fess and then into three columns of equal width. A pale is a thick stripe down the middle which could potentially be the same width as the middle column of the registered device. Both have azure in the upper left corner and alternate from there. These look a lot alike, so even though they are clear of each other (the submitted device has a primary charge- the pale, while the registered armory has no primary charge), they visually conflict.