Well last year I noticed my Remington Model 7400 Carbine 30-06 Springfield has been jamming after I shoot a shot. Is there a way of fixing his without a gun smith or should I just send it to him?

Wow, so many questions....

Does the fired shell complete eject from the rifle?

What type of shells are you using?  Soft Points?

Has rifle been properly cleaned?

I would guess that your ejector port shroud is either broke (plastic), or that you are shooting reloads.  The shroud being broke is a common problem with that model and some of them can be finicky if you are shooting reloads in them.  Just a couple of possibilities.

Remington Core Locts

first thing id do is a front to back side to side cleaning. take note as the bolt location. i had a 742 that jammed every third shot or so. i did a total scrub of the gun and dropped down from 180 gr's to 150 gr's and it shoots like a dream now.

i also installed a Sims LimbSaver Barrel De-Resonator. this thing may be the biggest hoax in the world but who knows.

I've worked at our local Rod & Gun Club's rifle range for 15 years as a range official, and your first step may be to go to your local range.  Many have NRA certified range officials, that while they aren't gunsmiths, may be able to spot your problem for you.  I know I've seen all kinds of things and many are very simple fixes, if you can actually see the rifle while its jammed.  You could also take it into your local gun shop where you purchased it.

After that, its probably time to break out your wallet and head for the gunsmith's.

Sorry, but its just too hard to figure out without a complete picture of what's going on.  Good luck.   :-/

Tap Rack Bang!  

Blow into the muzzle?

there is typically 2 causes of this on those models. Rusty chamber or bent guide rods.

Try a different ammo after cleaning the chamber extremely good.

Also try federal ammo.  Rem core locks tend to be on the weak side on pressures.