Solo PvP
Solo PvP is said to be a thing mostly abandoned by the greater Eve community, for myriad reasons and circumstance, some of which I am familiar with, and others that I am not. I don't buy that. As such, this article shall outline basic skills and tactics as they apply to solo and small gang PvP in lowsec.
The key is to find your fights, instead of waiting for them.
Why
Learning to solo PvP helps you develop a skillset that any FC will appreciate. You will become competent with using your d-scan, comfortable flying as a +1 skirmish or scout, and have a situational awareness that only comes from doing PvP. The losses you suffer are worth the ISK price you pay to become a better PvPer.
Ship Choice and Fitting
A frigate is cheap. Use that. Even t2 frigates won't break the bank, and you'll find your list of reasonable targets multiply if you fly them.
Active tank and afterburner.
Directional Scanning
Directional scanning is an amazingly useful thing to know how to do. You'll
I assume that you've taken the time to utilize the [Overview Guide]. A properly arranged overview is crucial to your ability to fight engagements. That being said, the Uni default overview does not lend itself well to scanning, as by default, most of your brackets are turned off. We'll remedy that.
To supplement the standard Uni overview, you can create a new preset in which near everything is selected. Planets, belts, etc... Save the preset as "Bracket" or something useful. Now, you can set your bracket profile so that all brackets pertinent to scanning are showing. They won't clutter up your overview, but simply give you something to scan towards while you're in space.
ROE or "Can I shoot that malefactor?!"
Assume everyone in space would love nothing more than to turn your beloved ship into charred wreckage. Even so, Eve University has a very strict policy about who you can engage first while in the University. I'll link it for you. Right here. Pay close attention to the fact that we can't engage neutral pilots first. If you land on grid with a neutral, feel free to target them or bump them, and make yourself a pest that deserves to be shot. Once they've shot you, they're fair game. The University does not consider any of these tactics aggress acts at the time of this writing. Point is: You can oftentimes goad a neutral pilot into a fight.
Gate and Station Guns
Don't fight on stations, unless you understand the mechanics of doing so.
Fighting on gates. Sometimes it's best to wait for a flashy to engage you first, in order to earn the sympathies of gate guns.
Gatecamps
They happen. If you're in a frigate, you'll usually survive. Sometimes you won't. If you jump into a gatecamp, spam your warp button.
Hunting Grounds
Barring yourself from doing certain things until you feel you meet certain prerequisites is a good way to hold yourself back. Let's skip that part. Find a good lowsec pocket with highsec access, and move there. Immediately. Drag some friends along, or speak to your CO (if you're ILN) about moving there as a squadron. Opportunities for solo and small gang abound when you live in lowsec.
A very good handbook was written that illustrates some good stomping grounds. It outlines lowsec pipes where a fight can often be found. Note that these pipes have ancillary pockets that are very cozy... Think about these pockets if you choose to move to lowsec.
This link will only work if you have ILN forum rights ---> The Pirate Hunter's Handbook
123 Now or "Let's shoot some shi... er, stuff!"
The example below uses small gang to illustrate my point only for the narrative flair that a Uni wardec allows for.
Ok. Let's start at the beginning. You're sitting in Aldrat, and the University has been wardecced by yet another pack of screaming fools calling themselves Mercs. Whatever. Let them flounder in the face of real PvP. You're bored, station spinning, and Alliance is just... sitting there. That blinky ain't gonna come soon.
As you're not comfortable FCing, let's do some small gang!
You'll have to assemble the requisite PvP fleet, which only needs to be 3 other pilots. Grab a few people that you're familiar with, and get in Vent. Now consider what ships you'll be bringing. I recommend frigates of the t1 or t2 variety, as they move quick, and warp quicker still. The fast warp is an extremely useful asset when you're hunting targets as a small gang or solo.
Useful Links
A handful of useful tips ---> [1] The blog of Azual Skoll ---> [2] Wensley's rifter handbook ---> [3]