Small Cabin

Basically, one wants to find what is previously on the document (and NEVER move a marker!), it was all there at the last certified survey so verify you know where the corners are and tape 'em with bright tape.
Once you know maybe you and the neighbors can walk and agree on the property lines? If so, maybe no survey needed. If not, the cost of survey due to contestment should be split.
Imo, a neighbor needs to know if you are going to survey. Having a neighbor come home and find new markers where they never were before makes for a potential bad situation. I am willing to 'give a few feet' (if needed) to have a good relationship with my neighbors!

I asked my surveyor when I was booking them (in Eastern Ontario). They said late fall/early winter was easiest. Leaves off for visibility. Some snow doesn't bother them, but too much hides stuff and makes finding pins and setting new ones a pain. Ditto completely frozen ground.

I work for a surveying company, assuming you are talking about a property boundary, then having the leaves off will help keep your costs down if your property is wooded.

Your advantage is you arent actually surveying an unsurveyed property, you are confirming the existing survey (same thing an expensive surveyor would do right off). The value to you doing this is that if you do need to hire one you can take them right to the markers which they will then confirm matches the property description.
One of the 'pins' will be the easiest to find. You have to have one defined point to work from. A real survey works clockwise but using the document and establishing one point you can go any direction 'around the map'. All the info is on the document and quite precise. The part many are confused about is the way the boundary lines are defined for the degrees/minutes/sec E/W, N/S, they dont sound logical to the common man but actually are not difficult; how to interpret them is online.
It is fair to make yourself a 'cheat sheet' map that makes sense to you and take detailed notes as you go, dont rely on memory. The orange tape 'flagging' left in place lets you return to a spot if/when you decide you proceeded on an error without totally starting over!
You should also be aware of and know how to deal with 'declination', the difference between magnetic north and true north. It changes over time! The bigger the property or longer the boundary the bigger the error can be.
You dont necessarily need a transit, though having one helps. I initially did 2 properties with a 'Forester's Compass' mounted on a walking stick and found all the corners. Have a helper (and communication between you), blaze orange 'flag tape' and some stakes, a long spool tape, a tall pole with blaze orange to spot from a distance for the helper while you 'sight'. Know how to do 'offset' around obstructions (visual and real) so you can deviate from the line and still return to it.
I find it to be challenging but great fun.