How to "decipher" the symbol for the recently announced doubly-charmed baryon?

The PDG naming scheme for hadrons is the authoritative source on this.

The easy bit is the superscript: that's just the charge. $++$ means a charge of $+2$.

The symbols for baryons are based on those chosen for the baryons formed of light quarks ($u$, $d$, $s$). They encode the isospin and quark content. The rules are relatively straightforward, but I'll refer you to the naming scheme for the full list.

A light-quark $\Xi$ has a quark content of $uss$ or $dss$. A heavy-quark $\Xi$ retains the single $u$ or $d$ and replaces one or both of the $s$ quarks with a $c$ and/or a $b$. This is denoted in the subscript: e.g. a $\Xi_c$ has $dsc$ or $usc$.

The +, - or 0 indicates the electric charge. The "c" stands for the charm quark indeed. Page 1 of the paper they give the three valance quarks of your baryon : ccu. They are all 2/3e as you can see on the wikipedia page of the quark, so you can check that you have a "++" baryon. For exemple the Xi baryon made of ccd has only one "+". https://en.wikipedia.org/wiki/Quark The Xi is for the family of baryon where you have at least one heavy quark. They are sometime called "cascade" https://en.wikipedia.org/wiki/Xi_baryon

dukwon is right, the PDG is a better source for particle physic.