Yugoslavia

Background

Pros:

Generous manpower pool and an exceptional manpower growth rate for a minor, enough for supporting your country into major status. Shortage of manpower is the downfall of many other minors.
Easy to max out central planning, meaning a small amount of IC can turn into a large amount of IC.
Proximity to other countries means the possibility for lightning fast conquests and great prospects
Generous starting army, although they are outdated and depleted.
Access to the Mediterranean sea, making an invasion of Africa and the Middle East possible.
OK tech teams, and by the time you annex your neighbors, you will have a powerful and well rounded mix of teams.
Decent ministers, the manpower chief of staff especially is useful for Yugoslavia moreso than a typical 20% org regain minister would be.

Cons:

Horrid generals, but by the time you get done with Italy, you will have an experienced officer corps
Outdated and worthless starting air force and navy
No transports
No merchant marine
Dependent on supply trades to maintain resource levels until she expands
Proximity to other countries and a tangled web of guarantees of independence means you will have to fight on multiple fronts during any war you choose to partake in, and will have to fight delaying actions within your own country while your offensive forces fight elsewhere.
In the latest DD/ARMA patch, you will have to devote the majority of your money to the intelligence system or be smothered by foreign meddling - this disables your ability to use the diplomacy system.

Strategy

The key to Yugoslavian supremacy is to conquer the dominions of Italy, this will propel you into major power status.
Disband your fleet, it is worthless. Set your air force to not reinforce or upgrade.
Start the game and build 4 IC, put all your divisions under logistic generals.
Move your sliders to central planning, when you can no longer move to central planning, move to authoritarian, then move to central planning again, by 1940 you should have +25% IC from central planning.
Technologies: Modern infantry, mountain divisions, cavalry, but most importantly: machine tools, agriculture, ground doctrines, rear area dumps.
Make sure you have the manpower chief of staff, and that you remove the -IC% minister ASAP.
The first 3 IC will finish first, you won't have enough IC to finish the fourth on time.
When the 3 IC finish, let your army reinforce and upgrade.
Trade supplies for energy/metal/rares from Germany if need be.
When this is finished, 2 serials of unbrigaded infantry, 1 serial of unbrigaded mountain troops, when the last IC finishes, 1 more serial of unbrigaded infantry and leave the rest IC for upgrades/reinforcements.
By Anschluss of Austria you should have at least 35 modern, reinforced divisions, enough to surprise Italy with an attack.
DO NOT DECLARE WAR ON ITALY DIRECTLY - Germany will likely declare war on you in retaliation. Instead, declare war on defenseless Albania, after making sure all but 1 of your divisions is on the Italian border. You will be able to annex Albania within 2 weeks - and meanwhile, Italy will declare war on you because it guaranteed the independence of Albania.
Invade Italy, they should be caught completely by surprise since up until that point you had good relations. They will begin to rush reinforcements from Africa. Before the reinforcements arrive you should have Genoa/Turin pocketed and have a firm defensive line at La Spezia.
When you approach 30-40 manpower (for me it was when I had ~45 divisions), stop building units and build a few transports and at least 3 parallel runs of convoys (these will be used to invade north Africa and eastern Africa). The remaining manpower will be used to reinforce losses and build the occasional unit.
Slowly push Italy into the boot, you will most likely not be able to encircle them and will push a battered army group into Sicily. Cross into Sicily by foot and wipe them out.
The Italian colonies should be COMPLETELY EMPTY - send a few divisions to capture the victory points there.
Once Italy is annexed, you should have about 73 IC and a new resource stockpile. Your biggest problem, which has probably become obvious to you, is a lack of manpower. From this point on, we are only going to build infantry when it is commandos (namely mountain), and even then, in small quantities. Build tanks from this point on, although you might not be up to tech until 1941. Tanks cost less manpower, and give you more bang for your buck. Do only build modern medium tanks, ancient tanks and light tanks are a waste of time and will take a substantial amount of time to upgrade.
I recommend making Libya and Somalia as puppets, they will augment your army with more infantry, and if you can deal with losing 1-2 IC, then also release Ethiopia. By the end of the year they will have 6+ divisions each, and if you released them with central planning all the way to the right, they should have 8-9 IC, not bad. If you notice your puppet countries' IC going down, make sure you supply them with rare materials, energy and metal, if need be. Even a small deficit can cripple a puppet nation and take away several IC.
Do not bother making military police/garrisons for Italy, it might seem tempting, but you would need a dozen or more garrisons to suppress the partisan revolt risk, and you simply don't have the manpower to do this.
Yugoslavia has now come into its own, but you are still missing several things to flesh out into a major power: an airforce, maneuver forces (tanks) and a navy. Focus on this now, especially the first two. 2-3 groups of interceptors should be enough to ensure local air superiority, while 1-2 groups of tactical bombers will prove to be extremely useful for operational elasticity. Most importantly, you need at least 2 corps (3 division armies) of tanks, preferably 3. These units will use up much less manpower to make than the infantry we were spamming previously and hence their manufacture will be orderly.
At this point, several major options are open to you. Joining the allies, you would open a second front against the Germans, which may result in the offensive against the low countries and France grinding to a halt. The underbelly of the Reich will be exposed and little will stand between you and Berlin. Alternatively, if for some reason your previous campaigns dragged past spring of 1940, and western Europe has already been invaded, joining the Axis would also offer an interesting option: a surprise attack across Africa would result in an immediate victory and the capture of the Suez, the eventual seizure of the Middle Eastern oil fields, while you could also augment the german Army Group South in its offensive against Stalingrad and Baku. If you don't want to make a major decision like this now, you could invade Hungary to gain some more IC - chances are, they didn't join the Axis and that the guarantee of independence on them is no more.
Tip: Do not attack Germany 1v1 - while you might think you could pull it off because most of your units are 2-3 stars now and your generals have gone from 1 skill to 4-5, it won't make up for Germany's numerical advantage, air superiority and doctrinal superiority. I would only recommend engaging Germany if the Western front is still intact or you are willing to military control your allies and bring reinforcements to your theater. If Germany seems impossible to take down, just join the Axis, you are fascist anyway and you wont need +200 relations to get a decent chance of joining up.
Tip: When you declare war on Germany, you will likely be attacked by Hungary, Romania and Bulgaria. My recommendation is to form a defensive line along the Austrian border, and Romania-Hungary, and devote the rest of your divisions to invading Bulgaria. You will have to give up Novisad and other provinces north of the Danube - it will be impossible to defend them. Consider military controlling some minor allies to help bolster your defensive line - Iraq is especially useful. It will probably be a 1:1 fight in Bulgaria (that's all you can spare and not have the rest of your country be over-run), but your experienced and modern troops will overpower the Bulgarians. It may seem like you are in a world of trouble, but if you can manage to annex Bulgaria, you will win the war.

[ ]{#Axis_or_no_Axis?} Axis or no Axis?

Entering the axis can be worthwhile, especially if you control Bulgaria and Albania. When you enter, you will receive the coup event. Ignore it and do not violate the pact of steel. Note that it'll get you a total of 20 dissent, or a DoW from Germany if you decide to break the pact.

Other option is to join the Comintern (The Allies are probably the worst choice, since they can't help you much). Joining the Comintern, SU might be able to help you by sending troops in your territory, plus you don't need to garrison a SU border you might have, freeing most (if not all) of your forces to fight Germany. Do this if you want more of a challenge.