This is a classic alliance for the southern triangle: two countries pair up versus number three, but an alliance with quite a few other implications on the board. The key for this alliance in the very early game is Galicia. After that, you would be looking for a quick death of Turkey and afterwards expand your powers quickly in northern and western region.
Although it does not happen very often, Russia and Austria can be great allies. They both have their own area of expansion, and they have common enemies and neighbors on the board. Why does it often happen that Russia and Austria find themselves on different sides? I believe there are a few reasons. One is that Austria considers Germany as its natural ally (which it is), and in a fight between Russia and Germany, Austria will pick the German side. Furthermore, the Turkish player will do everything in its power to prevent an alliance between Russia and Austria, to not lose the battle in the southern triangle. Thirdly, Russia will have many options for expansion, but will look at the Balkans as the most prominent one, and a Russian player in the Balkans is not compatible with a sizable Austria.
If you look at the way in which this alliance could work, Austria and Russia would have to start with either a DMZ or a bounce in Galicia. The goal at the start of the alliance is to quickly eliminate Turkey. However, if you have some experience or not, Turkey is quite difficult to quickly eliminate from its corner position. The key is to take Greece in fall 1901 with the Austrian fleet, so to make a move for AEG in spring 1902. For Austria to be able to do this, he could ask Italy for help in the form of a Lepanto move.
The minimum required for an elimination of Turkey is that Italy does not make a quick move against Austria, although you could withstand Italy knowing that Russia is on your side. If I would be convinced of my alliance with Russia, I would propose a bounce with Austria in Tyrolia with my army in Vienna.
For the Russian player, it is critical that Turkey is not allowed on the Black Sea. Best option is to agree on a bounce, while ideally you also ensure that Armenia is not occupied.
Again, in spring 1902, all the cards should be aimed at Turkey. If Russia manages to get two builds, building a fleet in Sevastopol should normally seal the deal. As this will give you firepower to take the BLA by force. With that build, it will be fully clear for Turkey you are coming, so do not waste too much energy on further diplomacy with Turkey. Another option is to conceal your intentions as Russia, build an army in Sevastopol, and move to Armenia.
In winter 1901, I would highly recommend to build a fleet in the Sevastopol and a fleet in Trieste, if this is possible. These fleets will seal the faith of Turkey. However, I can imagine that with only one of these fleets Turkey’s elimination can also be achieved. You will have to find a solution for these Russian fleets after the BLA is conquered; one possible way is to disband one fleet by letting Austria conquer Rum.
Assuming you are able to eliminate Turkey I would divide the spoils as follows: the Balkans for Austria, and Turkish home supply centers for Russia. So Russia gets Con, Smy, Ank. Austria gains Greece, Bul, and Rum. This change of Rum from Austria to Russia seems illogical, but it is the fairest way to divide the spoils. However, I hope you are familiar with the saying: “life is unfair, deal with it”.
After 1902, Russia can go and attack either England or Germany, and Austria can go against Italy. This is usually also the point the alliance fails, as Austria could be tempted to take the side of Germany and they decide they need to attack Russia. The only way to prevent this as Russia is by explaining to Austria the potential gains. He could have Munich and perhaps other supply centers, while Russia has gains in Scandinavia.
It is critical to spend time on this moment in terms of your diplomatic energy. If your Russia-Austria alliance is to last till the end you need a way forward for both, and most likely a strategic partner in the west to start working towards a three-way draw. This partner in the west would normally be France, but England could be possible as well.