The basic things you need to do when initiating a clinch are clear your opponent's hands, get better hip/head position and get the grips you want. Now that opens up a lot of questions, such as what are the grips you want? If you prefer clinches that offer head control, you're going to have more success with different techniques than if you prefer pummelling for underhooks or whatever else. Also, what rule set?
The easiest way to get into a clinch, whether you're short or not, is to throw a right hand while level changing and head butting your opponent's chest during the follow through. This leads into takedowns if you want, or lets you immediately start with dominant head position so you're a step ahead when you start grip fighting. Plus a lot of people will try to get collar ties when you do this (especially if they blocked the right) but getting your head in position will make sure they don't have room to get their elbows where they need them and they'll just give you free underhooks by trying if you keep pressing forward. Cormier did this to Mir, with or without the right hand, over and over.
I second the dipping jab suggestion. It can lead to a collar tie if they do nothing or slip inside, if they slip it outside you get head control and snap them down off balance.
Similar to the dipping jab, if you can bait them into throwing a wide right then you can jab inside it, block with your forearm or jam your palm into their bicep, all of which give you a collar tie shortly after. Just make sure to bend your knees!!
If they jab at you, parry it but follow through with the parry more than you would normally. Simultaneously bend your knees, step forward hard (forehead to chest) and shoot that parrying hand through for an underhook.
Another tactic is to extend your hands and start smothering theirs. The goal is to have your hands on top and outside of theirs. From there you don't have to worry about punches, and that hand fighting is part of clinching so hopefully you know how to work from there. A good rule of thumb is to get your hands on top and outside of your opponents. That means to hit you they either have to go down the middle (which makes it easy for you to parry and step in) or pull their hand away then go over yours which makes it easy to step forward and block inside to get collar ties as mentioned above. Matt Brown and Overeem do versions of this.
If your opponent keeps their gloves against their heads and don't reach out to hand fight with you, physically grab (if you're in mma gloves) them or push them up and into the opponent. You can use this to walk them backwards to the ropes, push them into kicking range, off balance them to create openings for your clinch entries, etc. The only thing they can really threaten with is a teep. If they pick up a leg, steering wheel their arms towards that side and they should be forced to put the leg back down or fall over.
These are just some general ideas to play around with. Some of them involve hitting the other guy, but specifically not wanting to do that because you have short arms seems like a defeatist attitude to me.
