In order to check how many wins you have, go to Barracks, then go down to Combat Record. Hovering over the Multiplayer tab, it will show how many wins you have (You must be level 10 to see this). To long time players of Call of Duty, or even most online shooters, this guide won't teach you very much. However, instead of telling you to "just play the game, it will unlock naturally", I will point out many things that both newcomers and experienced players can learn from to potentially speed up the process.
Game Modes: Your best bet for game modes if you are less experienced or just want to play the objective is either Hardpoint or Domination. I will outline strategies for both of these modes, as well as Free For All, which I only recommend for experienced players. However, Free for All does not require you to rely on teammates so do not feel discouraged from playing that mode.
Domination: Make sure you do not hold all 3 zones unless you are either losing by a significant amount or if you already are about to win. Spawns may flip which can lead to your whole team dying and allow the other team to easily grab 2 zones. Always have your spawn point (either A or C) and B.
Hardpoint: Self explanatory, hold the point and defend it. Unlike previous entries, the next hardpoint will show up with 10 seconds left on the current one. Make sure to head over to the point so that you can hold it before enemies get over. A lot of the time you can score easy points without any effort if you make sure to get to the point. When a team is on the point, the match timer will pause. Any time that neither team is on the point will make the match timer to resume, so if the time is almost up and your team is winning with a good amount away from 250 points, let the time run out.
Free For All: This is the mode that I recommend the least, however if you are good then matches can be short since you need 30 kills to win. You are best off sticking with the other 2 modes above, but I know some do not like putting up with teammates.
Scorestreaks: In this game, scorestreaks persist through death, but cost much more. I could not find myself scoring enough for the higher streaks, which makes the Care Package more valuable in this games than others in my opinion. Spy Plane, Care Package, and Cruise Missile are what I personally use, but if you don't like the Care Package, you could swap it out for Artillery. The reason I point scorestreaks out is so that you can clear objectives of players in order to either protect an objective or to be able to take over an objective.
Create-A-Class: When playing the objective, what you use to kill people generally doesn't matter as much, however SMGs dominate for the most part. I personally used the MP5 and the AK-74u, and although attachments are not required, you may want attachments that give you more ammo (extended mags) and recoil control (Foregrips). There is a lot of specific statistics that are shown aside from the bars on the bottom going up and down on the bottom of the screen, allowing you to really create your loadout to more suit your style more than before.