I'm using an Arduino to switch an led strip on and off. I have a 5v 4a power supply for the leds. I've tried doing this with the transistors that came with my Arduino starter kit (2N 2222A -H331) but the result is that the led strips are significantly dimmer when switched on by the Arduino than if I just touch them directly to the power supply.
I'm new to this and I haven't been able to find anything very helpful online that explains how to select an appropriate transistor for my project. What do I need, and as a secondary question, how do I know what I need without asking the forums every time?
Ensure that your transistor is rated for continuous current significantly higher than your intended load (30-50% headroom minimum IMO), and that the Rds(on) is nice and low, and that it is spec'ed for 4.5v logic level on the gate (it will specify Rds(on) with Vgs=4.5v if it is).
I normally default IRF3708PBF, because it's an easy to work with through-hole package, works with even 3.3v on the gate (so I don't need to stock two fets, one for 5v projects and another for 3.3v ones), and is capable of holding off up to 30v (more than most projects will touch) and handling more current than you'd normally ever want or need to. There are of course cheaper choices that will suit your purposes just fine, since you're not driving more than a few amps (or 1.x amps per channel if it's RGB), and you don't care about using 3.3v on the gate. 4A is touching the range at which you might be able to get away with SOT-23 fets; some of those have absolutely mindbogglingly good specs for something the size of a rice grain. I think a DMN1019 would do it, for example (hey, funny thing, I just happen to sell SOT-23 breakout boards - bare and assembled with DMN1019 as one of the options); the reason I say that one is that (partly because it's only good up to 12v, so the other specs end up better) it offers insanely low resistance with 5v on the gate, so heat dissipation is unlikely to be an issue.
Your transistor is a low power BJT; even high power BJT's will drop a significant voltage even in saturation, and yours is not meant for large loads; see the datasheet. Always read and understand the datasheet for parts you're using.